It means that little Sassuolo will play in the Europe for the first time in their history next season after their sixth-place finish ahead of the Rossoneri in Serie A.
That is all from the Stadio Olimpico for tonight though.
Join us tomorrow for live text commentary on a tasty Copa del Rey final between Barcelona and newly-crowned/perpetual Europa League champions Sevilla.
Post update
AC Milan 0-1 Juventus
A historic couple of seasons at Juventus for Massimiliano Allegri.
For his former club - AC Milan - it is a 2016-17 campaign without continental football to look forward to.
FULL-TIME
AC Milan 0-1 Juventus
The double double is done.
Getty ImagesCopyright: Getty Images
CLOSE!
AC Milan 0-1 Juventus
Jose Mauri from 20 yards!
A thumped shot...and into the hoardings! Just wide!
Post update
AC Milan 0-1 Juventus
Davide Rugani clips Mario Balotelli out on the left wing.
Booking for the Juventus defender and goalkeeper Gianlugi Donnarumma is up from the back for the set-piece!
Post update
AC Milan 0-1 Juventus
Three minutes of added time at the end of extra time.
Mario Balotelli lining up a free-kick from out near the corner flag.
Plenty of whip on his delivery, but not enough height and the black and white boots clear.
Post update
AC Milan 0-1 Juventus
Things are suddenly getting niggly.
Alvaro Morata gets into a shoving match with Jose Mauri. Both are booked and the officials have to act fast to keep the nearby Juventus bench from wading in to defend their man's honour.
PENALTY APPEAL
AC Milan 0-1 Juventus
Big shouts from the Rossoneri.
But replays show that Keisuke Honda has flopped rather easily over Giorgio Chiellini's planted leg.
He's looking for that at the very least.
Chiellini gets booked for his vigorous protests of innocence - and Honda's guilt.
Post update
AC MIlan 0-1 Juventus
Juventus are nibbling down the clock now.
Their fans are bouncing. AC Milan's have 1000-yard stares on.
The Berlusconis look on with thunder in their brows.
Post update
AC Milan 0-1 Juventus
If ever it was Mario time...
AC Milan shove on Mario Balotelli in place of Juraj Kucka.
Rabbit out of hat time now. Does Balotelli still have those sort of tricks up his sleeve?
GOAL - Alvaro Morata
AC Milan 0-1 Juventus
Lethal.
Alvaro Morata has been on the pitch about two minutes and shows more finishing chops than the rest of the players on show combined.
The Juventus striker drills home a sweet 15-yard half volley from Juan Cuadrado's cross. Gianlugi Donnerumma has no chance.
Juventus are 10 minutes from a historic double double.
Getty ImagesCopyright: Getty Images
SUBSTITUTIONS
AC Milan 0-0 Juventus
Both teams tweak things up in preparation for penalties and to try and mop up some of the lactic flowing around out there.
Juventus bring on striker Alvaro Morata in place of midfielder Hernanes.
Milan bring off skipper Riccardo Montolivo and introduce Jose Muari.
HALF-TIME IN EXTRA-TIME
AC Milan 0-0 Juventus
On we go.
That is another 15 minutes of goalless football under our belts.
"Next goal wins"? I think we have been playing those rules pretty much from 60 minutes on.
EPACopyright: EPA
YELLOW CARD
AC Milan 0-0 Juventus
Tired legs and tired minds adds up to mistimed challenges.
Andrea Barzagli blunders in and gets booked.
FULL-TIME
Paris St-Germain 4-2 Marseille
Getty ImagesCopyright: Getty Images
All over in Paris. Zlatan Ibrahimovic gets the big send-off he wanted, and the goals he craved. PSG complete a clean sweep of domestic trophies: Ligue 1, Coupe de France, Coupe de la Ligue, Trophee des Champions.
Probably the least tense of today's five cup finals across Europe, but no less memorable for that.
YELLOW CARD
AC Milan 0-0 Juventus
AC Milan pick up another yellow card for a needless foul by M'Baye Niang. Paul Pogba brings a good save out of Gianluigi Donnarumma shortly after.
Mario Balotelli is lacing them up on the AC Milan bench...
ReutersCopyright: Reuters
Post update
Paris St-Germain 4-2 Marseille
Post update
Bayern Munich 0-0 Borussia Dortmund (4-3 pens)
The Bayern fans are bouncing in Berlin. Their team did just about deserve it over 120 minutes; Dortmund merit great credit for the way they hung in there, though. It was not a classic cup final; it was more of a slugging match. But Bayern found a way to win.
ReutersCopyright: Reuters
Post update
Paris St Germain 4-2 Marseille
Zlatan Ibrahimovic is heading off early for a full ego massage.
The Paris St Germain striker departs to be replaced by defender Layvin Kurwaza and even the PSG subs are summoned to their feet to applaud off the totemic Swede.
Lordy, this is the biggest farewell tour since Led Zepplin.
Bayern win the DFB-Pokal
Bayern Munich 0-0 Borussia Dortmund (4-3 pens)
Pep Guardiola weeps tears of joy. There are tears of despair for Dortmund's players. Guardiola leaves Bayern with a domestic double. Dortmund, who have suffered their fair share of agony this season, end Thomas Tuchel's first campaign as manager empty handed. For them, it is a third successive German cup final defeat.
Live Reporting
Mike Whalley and Mike Henson
All times stated are UK
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ReutersCopyright: Reuters
Latest PostPost update
AC Milan 0-1 Juventus
It means that little Sassuolo will play in the Europe for the first time in their history next season after their sixth-place finish ahead of the Rossoneri in Serie A.
That is all from the Stadio Olimpico for tonight though.
Join us tomorrow for live text commentary on a tasty Copa del Rey final between Barcelona and newly-crowned/perpetual Europa League champions Sevilla.
Post update
AC Milan 0-1 Juventus
A historic couple of seasons at Juventus for Massimiliano Allegri.
For his former club - AC Milan - it is a 2016-17 campaign without continental football to look forward to.
FULL-TIME
AC Milan 0-1 Juventus
The double double is done.
CLOSE!
AC Milan 0-1 Juventus
Jose Mauri from 20 yards!
A thumped shot...and into the hoardings! Just wide!
Post update
AC Milan 0-1 Juventus
Davide Rugani clips Mario Balotelli out on the left wing.
Booking for the Juventus defender and goalkeeper Gianlugi Donnarumma is up from the back for the set-piece!
Post update
AC Milan 0-1 Juventus
Three minutes of added time at the end of extra time.
Mario Balotelli lining up a free-kick from out near the corner flag.
Plenty of whip on his delivery, but not enough height and the black and white boots clear.
Post update
AC Milan 0-1 Juventus
Things are suddenly getting niggly.
Alvaro Morata gets into a shoving match with Jose Mauri. Both are booked and the officials have to act fast to keep the nearby Juventus bench from wading in to defend their man's honour.
PENALTY APPEAL
AC Milan 0-1 Juventus
Big shouts from the Rossoneri.
But replays show that Keisuke Honda has flopped rather easily over Giorgio Chiellini's planted leg.
He's looking for that at the very least.
Chiellini gets booked for his vigorous protests of innocence - and Honda's guilt.
Post update
AC MIlan 0-1 Juventus
Juventus are nibbling down the clock now.
Their fans are bouncing. AC Milan's have 1000-yard stares on.
The Berlusconis look on with thunder in their brows.
Post update
AC Milan 0-1 Juventus
If ever it was Mario time...
AC Milan shove on Mario Balotelli in place of Juraj Kucka.
Rabbit out of hat time now. Does Balotelli still have those sort of tricks up his sleeve?
GOAL - Alvaro Morata
AC Milan 0-1 Juventus
Lethal.
Alvaro Morata has been on the pitch about two minutes and shows more finishing chops than the rest of the players on show combined.
The Juventus striker drills home a sweet 15-yard half volley from Juan Cuadrado's cross. Gianlugi Donnerumma has no chance.
Juventus are 10 minutes from a historic double double.
SUBSTITUTIONS
AC Milan 0-0 Juventus
Both teams tweak things up in preparation for penalties and to try and mop up some of the lactic flowing around out there.
Juventus bring on striker Alvaro Morata in place of midfielder Hernanes.
Milan bring off skipper Riccardo Montolivo and introduce Jose Muari.
HALF-TIME IN EXTRA-TIME
AC Milan 0-0 Juventus
On we go.
That is another 15 minutes of goalless football under our belts.
"Next goal wins"? I think we have been playing those rules pretty much from 60 minutes on.
YELLOW CARD
AC Milan 0-0 Juventus
Tired legs and tired minds adds up to mistimed challenges.
Andrea Barzagli blunders in and gets booked.
FULL-TIME
Paris St-Germain 4-2 Marseille
All over in Paris. Zlatan Ibrahimovic gets the big send-off he wanted, and the goals he craved. PSG complete a clean sweep of domestic trophies: Ligue 1, Coupe de France, Coupe de la Ligue, Trophee des Champions.
Probably the least tense of today's five cup finals across Europe, but no less memorable for that.
YELLOW CARD
AC Milan 0-0 Juventus
AC Milan pick up another yellow card for a needless foul by M'Baye Niang. Paul Pogba brings a good save out of Gianluigi Donnarumma shortly after.
Mario Balotelli is lacing them up on the AC Milan bench...
Post update
Paris St-Germain 4-2 Marseille
Post update
Bayern Munich 0-0 Borussia Dortmund (4-3 pens)
The Bayern fans are bouncing in Berlin. Their team did just about deserve it over 120 minutes; Dortmund merit great credit for the way they hung in there, though. It was not a classic cup final; it was more of a slugging match. But Bayern found a way to win.
Post update
Paris St Germain 4-2 Marseille
Zlatan Ibrahimovic is heading off early for a full ego massage.
The Paris St Germain striker departs to be replaced by defender Layvin Kurwaza and even the PSG subs are summoned to their feet to applaud off the totemic Swede.
Lordy, this is the biggest farewell tour since Led Zepplin.
Bayern win the DFB-Pokal
Bayern Munich 0-0 Borussia Dortmund (4-3 pens)
Pep Guardiola weeps tears of joy. There are tears of despair for Dortmund's players. Guardiola leaves Bayern with a domestic double. Dortmund, who have suffered their fair share of agony this season, end Thomas Tuchel's first campaign as manager empty handed. For them, it is a third successive German cup final defeat.