Schneiderlin joined the Toffees in a £20 million deal on Thursday.
Schneiderlin ended his unhappy spell at Manchester United by completing a £20 million move from Old Trafford on Thursday.
The France international has found himself completely frozen out by Jose Mourinho in recent weeks, and he has made just three Premier League appearances all season.
However, he has now embarked upon a fresh start on Merseyside which will see him reunite with the man he so loved playing under at Southampton.
Koeman is clearly delighted to have secured his top transfer target, and believes that Schneiderlin's desire to impress for Everton will prove just as important as his obvious technical ability.
Koeman told the club's website: "I’m very pleased because I know the player, I know the qualities of the player, I know him as a person and he’s really desperate to come to Everton - and that’s what we need. We want good players but we also want players who really want to show their qualities in front of the fans of Everton.
"He’s a strong character. I worked with him for one season at Southampton and he’s a midfield player who can play in different positions in the midfield. He’s also a fast player, he’s a clever player and he’s a personality. Normally, he’s part of the French national team and at 27 years old he’s part of the future at Everton.
"Morgan is really hungry to show his qualities and to play because that is the best thing for a football player. You are born as a football player to play games, not to sit on the bench or not be part of the team. But this is a new step, it’s a new future and he will show his qualities. I am convinced of that."
Koeman will be hoping that Schneiderlin has what it takes to transform the fortunes of the club's midfield.
The Dutch boss has been fairly public in his criticism of players such as James McCarthy as not being good enough for the standard he wants to set, and securing Schneiderlin will go a long way to solving that problem.