Manchester City's FA Cup semi-final against Brighton will be played on Saturday 6 April at 17:30 BST and broadcast live on the BBC.
The other semi-final tie between Watford v Wolverhampton Wanderers will take place a day later at 16:00 BST and be broadcast on BT Sport.
The Football Association has said each of the four clubs will be given about 33,000 tickets for their own fans.
Ticket prices will remain at £30, £45, £65 and £80 for adults.
Manchester City's game with Brighton, which takes place on the same day as the Grand National, and starts just 15 minutes later, will be broadcast on BBC One, BBC Radio 5 Live and the BBC Sport website.
Pep Guardiola's side, who are chasing an unprecedented quadruple, reached the last four thanks to a comeback win against Swansea in the quarter-finals.
They beat Brighton 2-0 in their Premier League match in September.
Their FA Cup semi-final will take place three days before City visit Tottenham's new stadium for the first leg of their Champions League quarter-final.
Wolves, who beat Manchester United 2-1 in the FA Cup quarter-finals, are a point and a place above eighth-placed Watford in the Premier League.
But Nuno Espirito Santo's side lost 2-0 at home to Javi Gracia's Watford in the league in October.
The FA said Wembley Stadium ends have been allocated to the clubs and their fans in consultation with the local transport and police authorities.
They are as follows:
- Manchester City (East) v Brighton & Hove Albion (West)
- Watford (West) v Wolverhampton Wanderers (East)