Newport assistant manager Scott Young, himself a former Cardiff player, said he was sorry to lose the promising Green.
"He's still young lad but he's got a lot in his locker and he has a chance to make it at a higher level," Young told BBC Sport Wales.
"Matt's a big loss to us when we are looking for promotion, but I can understand his decision and wish him all the best.
"I told him to get his head down at Cardiff, knuckle down, and see where it takes him."
Green told www.cardiffcityfc.co.uk "It's amazing, a dream come true. I'm really excited, but it's a big step up and I have a lot to prove."
Going out of Ninian Park is Luigi Glombard. The Frenchman has signed for Leicester on a months loan.