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, with Adama Traore having swapped for Villa for Premier League side Boro in a separate deal.
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.