The FA Cup semi-final between Brighton and Manchester United will be shown live on BBC One on Sunday, 23 April, with kick-off at 16:30 BST.
The other tie – between Manchester City and Championship side Sheffield United, also at Wembley – will be live on ITV1 on Saturday, 22 April (16:45).
Brighton have not reached the final since they lost 4-0 to Manchester United in a replay in 1983.
The Red Devils are 12-time FA Cup winners and Carabao Cup holders.
Sheffield United – the lowest-ranked club left in the competition – are four-time winners of the FA Cup, though their last triumph was in 1925.
Manchester City, who are in the Premier League title race and quarter-finals of the Champions League, are looking to win the FA Cup for a seventh time.
The final of the FA Cup is at Wembley on 3 June.