The 28-year-old Ghana international has penned a four-year contract with the Championship club.
It is the second piece of business done between the two clubs on deadline day – Adama Traore having swapped for Villa for Boro in a separate deal earlier on Wednesday.
Adomah helped Boro to second place in the Championship last season, scoring eight goals in 47 appearances, and has played twice in the Premier League for them this term.
Villa boss Roberto Di Matteo said: “Albert is a player I’m really happy to have brought to the club and like others he knows what is required to win promotion from the Championship.
“He is an attacking player who creates goals and I’m confident he will be an impressive addition to the group.”
Villa have been spending big this summer as Di Matteo bids to lead the club back to the Premier League at the first attempt.
Jonathan Kodjia signed from Bristol City in a deal which could rise to £15million on Tuesday and Ross McCormack cost around £12million frm Fulham earlier in the window.