The England Under-21 international has produced some sparkling performances for the Whites in recent years and is regarded as an exciting prospect for the future.
A number of Premier League clubs were interested in securing his services but Villa have now won the chase for the 19-year-old.
Delph underwent a medical a medical earlier on Tuesday before agreeing personal terms at Villa Park.
Details of the deal have not been revealed but it is believed the fee could be worth up to £8million including add-ons.
Delph revealed that the club's reputation as a proving ground for young English talent, coupled with Martin O'Neill's track record, made committing to Villa an easy decision.
He told AVTV: "There are a lot of young English players here, an absolutely superb manager and this is the club I've chosen to play for so hopefully I can do well.
"I'm absolutely delighted. It's a big step up but I'm looking forward to it and hopefully I can do well.
"I've managed to get the move here and I'm going to work my hardest and hopefully the gaffer will give me the opportunity to play.
"I've been to look at the ground and it's absolutely unreal. It's mind blowing.
"If I get the chance to play in it and do well I'll be really chuffed with myself."
Aston Villa 8/13, Draw 12/5, Wigan 4/1