Koeman was announced as Toffees boss earlier in the week, after he agreed to a move from Southampton.
The Dutch boss’s arrival at Goodison Park has raised optimism around the Merseyside club.
And Distin, who played for six years at Everton between 2009 and 2015, said: “I think he will do well. I think it’s the right appointment for the club. The club needs some stability, and I think he’ll bring that to the club.”
Koeman initially stated that he did not want an Everton move, and insisted that he would stay with Southampton.
However, after Everton promised him a massive transfer budget, his head was turned and he agreed to a move.
The Toffees are now aiming to claim a European spot next season, with Farhad Moshiri set to invest heavily in the club.
Everton finished last season in 11th place in the Premier League, meaning that Koeman has a tough job on his hands to guide his new side into the top six.