Andre Ayew gave Swansea City a 1-0 first-leg advantage over the weekend, but the Swans couldn’t hold on to the first leg win as they lost 3-1 in the second leg to exit 3-2 on aggregate.
Brentford have therefore booked a place in the final to be played at Wembley
Ollie Watkins' composed finish in the 11th minute levelled the semi-final on aggregate, and a header from Emiliano Marcondes put the Bees ahead in the tie four minutes later.
Bryan Mbeumo volleyed in a cross from Rico Henry in the first minute of the second half to make it 3-0 on the night and give Brentford a two-goal cushion.
Rhian Brewster dragged Swansea back into the contest with 12 minutes remaining, capitalising on a poor clearance from Pontus Jansson and chipping home goalkeeper David Raya, but the visitors were unable to find a second goal which would have forced extra-time.
Victory meant the Bees signed off at Griffin Park, their home of 116 years, in style before their move to a new stadium this summer.
The west Londoners, who are looking to end their 73-year exile from the top flight, will face either Cardiff City or neighbours Fulham at Wembley on Tuesday, 4 August.