The 21-year-old had been a key target for Villa boss Dean Smith, who managed the England Under-21 centre-back when he was in charge of the Bees.
Konsa played 47 times for Brentford after a £2.5m move from Charlton in 2018.
"He's a high-potential player who I believe can step up to the Premier League and I'm really looking forward to working with him again," said Smith.
Konsa will join up with the Villa squad on Thursday when they fly to the United States to continue their pre-season work.
Villa have prioritised strengthening their defence having also signed Tyrone Mings, 26, from Bournemouth while still exploring the possibility of re-signing Manchester United's Axel Tuanzebe, 21, on loan.
Tuanzebe helped Villa to promotion back to the Premier League via the Championship play-offs.