Everton have signed Wales captain Ashley Williams from Premier League rivals Swansea for an undisclosed fee, thought to be £12m.
They are also in talks to sign Crystal Palace midfielder Yannick Bolasie and Sunderland defender Lamine Kone.
"I believe the club is going in the right direction," said Williams.
The defender, who has agreed a three-year deal with the Merseyside club, said he was keen to work with former Netherlands international Koeman.
"He's been one of the greatest centre-halves to ever play the game, so I look forward to learning from him," Williams told the club's website.
Swansea had rejected an earlier £10m bid from Everton.
The signing comes a day after England defender John Stones left Goodison Park to join Manchester City for £47.5m.
Williams featured in Wales' run to the semi-finals of Euro 2016 and has not played any pre-season games following an extended break.
He spent eight years with the Swans, playing more than 300 games after joining for £300,000 from Stockport in March 2008.
As well as seeking deals for Ivory Coast international Kone and DR Congo's Bolasie, both 27, Everton are also determined to keep Romelu Lukaku.
The 27-year-old Belgium striker has three years remaining on his contract at Everton, and is reported to be interesting his former club Chelsea.
Dafydd Pritchard, BBC Wales Sport:
While Swansea were reluctant to sell, it is understood Williams was eager to move as he sought a "new challenge".
With forward Andre Ayew also leaving for West Ham just a year after signing for the Swans, a source close to owners Jason Levien and Steve Kaplan said the Americans are insistent Swansea "will not become a stepping-stone club".