The former England midfielder underwent a medical at Villa's Bodymoor Heath training ground on Tuesday, having been released by West Ham at the end of last season.
Villa subsequently announced the 32-year-old's arrival via a short message on their official Twitter account, which read: "A big claret and blue welcome to our new signing Joe Cole."
In an interview with Sky Sports News, Cole revealed that manager Paul Lambert had earmarked a role for him in the centre of midfield.
He said: "It is a massive opportunity for me, I am delighted to be here.
"I spoke to the gaffer and we agree on a lot of things - playing in centre midfield sold it to me.
"They have a lot of young lads who will kick on, so I am really excited to be here. I will try and make some goals (and) score some goals. I'm looking forward to the challenge."
Cole made only six Premier League starts for West Ham last season, featuring as a substitute on 14 further occasions.
The second of his two stints at West Ham followed spells with Chelsea and Liverpool, in addition to a season on loan at French club Lille.
