New head coach Neil Lennon must get Hibernian promoted from the Championship in his first season, former Scotland winger Pat Nevin says.
Stubbs twice failed to gain promotion to the Premiership but did end Hibs' 114-year wait to lift the Scottish Cup.
"He has to get them up that first season," Nevin said of Lennon.
"I think he will. It is going to be a tough season ahead for Hibs. Another season in the Championship. We have got Dunfermline, Dundee United, Falkirk down there.
"It is not going to be easy to get out of that, and that is what his job is going to be.
"If they are good enough they will get up and he will go into that pantheon of managers who are dearly loved at Hibernian."
'A great fit'
This will be a third managerial stint for Lennon following contrasting levels of success during spells at Celtic - where he won five trophies - and financially troubled Bolton Wanderers, who were relegated from the English Championship shortly after he left in March.
"He didn't go through good times [at Bolton], but I would not blame that on Neil Lennon," former Chelsea and Everton player Nevin told BBC Scotland.
"It just shows how high you can go, and how low you can go in a short period of time if you are a manager.
"If he waited much longer, he may well become the forgotten man. He had to get another decent profile job. Oddly enough, I think it is a great fit for him.
"He is still quite young, I think there are still opportunities for him out there and he is quite respected by a lot of people down south. It's not last chance saloon but it will really help his profile if he does a good job.
"Alan Stubbs did a good job at Hibs and he gets the Rotherham job - and that is the sort of thing Neil Lennon will be thinking about.
"As for Hibernian, they have got a manager who knows and understands the Scottish system, understands what kind of club Hibernian are. And also, with a bit of luck for Hibs fans, he will keep that good relationship with Celtic going.
"There are players who played for Hibs on loan from Celtic last season who had a massive effect, especially in the Scottish Cup final."
That relationship resulted in Anthony Stokes and Liam Henderson spending time on loan at Hibs from Celtic.
And Hibs fan Nevin also believes Lennon will use his knowledge of the English Championship to bolster the club's squad.
"He must have had a good look at players all around that division," added Nevin.
"Maybe one, two or three of them can come up and make the big difference."