Hull will play Sheffield United in the other match at Wembley.
The Gunners most recent trophy came in 2005 when they defeated Manchester United on penalties at Cardiff's Millennium Stadium to lift the FA Cup and they booked their place in the last four after thrashing Everton 4-1 on Saturday.
Hull earned their place at Wembley with a 3-0 victory over Sunderland on Sunday to line up an all-Yorkshire clash against Sky Bet League One side Sheffield United.
In beating Charlton 2-0, the Blades became the first club from the third tier to reach the semi-finals of the competition since Wycombe in 2001.
Sheffield United manager Nigel Clough was a losing finalist at Wembley in the 1991 FA Cup final as a player with Nottingham Forest and he will be aiming to take his side all the way to the final, with a Yorkshire team guaranteed a place thanks to Sunday's draw.