The final will take place at Wembley on Saturday 17th May.
The exact kick-off time is to be confirmed, while the match will be broadcast live in the United Kingdom on both the BBC and ITV. Full ticketing details are also to be confirmed in due course.
It will be the third FA Cup final in Palace history, after 1990 and 2016, which also both took place at Wembley.
Manchester City booked their spot with a 2-0 win over Nottingham Forest in the second semi-final on Sunday, with goals from Rico Lewis and Joško Gvardiol, just under 24 hours after Palace had seen off Aston Villa in emphatic style.
Palace and City have already met twice this season in the Premier League. The first meeting at Selhurst Park was a thrilling 2-2 draw, with the Eagles losing 5-2 in the return fixture at the Etihad Stadium last month.
The two sides last met in the FA Cup back in the Fourth Round in January 2017, with City going through on that occasion.