Derby beat Leeds United 4-3 on aggregate, becoming the first Championship team to progress to Wembley after losing the first leg at home.
Trailing 1-0 before kick-off, the Rams went further behind at Elland Road, but pulled level through goals by Jack Marriott and Chelsea loanee Mason Mount.
Harry Wilson, who is on loan from Liverpool, put Derby ahead on aggregate but Leeds pulled level again before Marriott struck the decisive goal with five minutes remaining.
Villa sealed their passage to Wembley on penalties at West Bromwich Albion after their semi-final ended 2-2 on aggregate.
The winning penalty was struck by Tammy Abraham, also on loan from Chelsea.
It will be Villa’s second consecutive playoff final after losing to Fulham last season. They will hope to end a three-season absence from the Premier League.
Derby, managed by Frank Lampard, are looking to end an 11-year absence from the Premier League in their first playoff final for five years.
The Wembley final will also mark a reunion for Lampard and former Chelsea team-mate John Terry, who is assistant head coach at Villa.