The 25-year old completed his free transfer to Everton on Wednesday after leaving Manchester United and new teammate Jagielka is looking forward to working alongside the midfielder.
Cleverley enjoyed a fruitful loan spell at Aston Villa last season and Jagielka is now hoping he can bring that form with him to Goodison Park for the 2015/16 campaign and beyond.
"He's really excited to come here because it is a fresh start for him," he told evertontv.
"It was nice that he had the chance to go out on loan last season because things weren't going too well for him at Manchester United.
"He proved a lot of people wrong at Aston Villa - he obviously scored against us which I am sure he will take a little bit of stick for when he comes in.
"He's a really good addition. He's a great player - nice and tidy - and will fit into the manager's thoughts very well. He can play in a number of positions as well.
"He played in the positive and negative times at Manchester United and that's going to help him as a character and to blossom as a player.
"He played in an FA Cup final not too long ago and he's got quite a few England caps as well, so he has a lot of experience for a young man. It's something we can use to our advantage.