The midfielder completed a move to Everton from Aston Villa on Tuesday.
Gueye completed a move to Everton on Tuesday, signing a four-year deal at Goodison Park.
He arrives after the Blues activated the £7.2 million release clause in his contract at Villa Park last week.
He has become the club’s second signing of the summer, joining goalkeeper Maarten Stekelenburg in making the move to Merseyside.
His move sees him finally linking up with Koeman, who attempted to sign him last summer while in charge of Southampton, only to see Villa secure him instead.
And he has shared his delight at getting his man this time around, saying he will add quality to Everton’s squad from the outset.
“Idrissa will provide quality in our squad in the midfield and we want to increase the quality in the team,” he told the club’s official website.
“He was one of the players last season with the best record in interceptions and pressing in the midfield. We need this kind of quality and I’m happy to have him joining our club.”
Koeman will now be hoping that Gueye can replicate the kind of form he showed at Villa next season.
The midfielder was second only to Leicester City star N’Golo Kante in several areas last year, which is an impressive feat for a player whose team were eventually relegated.
Alongside a better standard of player at Everton there is every chance he will shine and Koeman will be hoping that proves to be the case.