Unai Emery had been working on a move for Gomes ever since Tielemans completed his bold exit to Manchester United - after the Red Devils activated his £35M release clause - with Villa also without Amadou Onana until 2027, following an ACL injury at the 2026 FIFA World Cup.
However, with UEFA Champions League football returning to Villa Park this season, Emery has been given money to spend on new players including a club record fee of £50M+ for Switzerland international Johan Manzambi from SC Freiburg.
Gomes is on course to slot straight in Villa's midfield alongside Manzambi after making 130 appearances in three and a half top-flight seasons at neighbours Wolves.
The details of Gomes' transfer include an an initial £34M fee paid up front, with £4m in add-ons, based on his performance across a long-term contract.
Villa's capture of Gomes is a real transfer coup for Emery, as the club were quicker off the mark for the Brazil international than Atletico Madrid, and he will now join up with his new teammates for preseason.
Emery's team will play three Europe-based friendlies this month before a three-match tour of Asia in August.