Young scored 22 goals in 83 starts for Watford.
He told the Villa website: “This is an exciting opportunity and I can’t wait to get started.
“I’m glad it’s all done and dusted with the medical and I can’t wait to train.
“There’s a good set of boys here and I just want to get down to work now. We’ve got a break next weekend, which is disappointing.
“But I can get to know the lads and prepare for a debut at Newcastle next week – that’s not a bad stage to make my debut.”
Young turned down a chance to join West Ham earlier this month.