One half of the duo Simon and Garfunkel, Simon pursued a successful solo career after they split in 1970, and is famous for hits such as 50 Ways to Leave Your Lover and You Can Call Me Al.
His first UK concert was a Simon and Garfunkel show with partner Art Garfunkel in 1964.
This summer's BST concert, offficially billed as Homeward Bound: The Farewell Performance, will not only be his last UK gig but will also mark the end of his tour for his 2016 album Stranger to Stranger.
Promoting the album after its release, Simon told the New York Times: "Showbiz doesn't hold any interest for me … I am going to see what happens if I let go. Then I’m going to see, who am I?
"Or am I just this person that was defined by what I did? And if that’s gone, if you have to make up yourself, who are you?", hinting that this might be his last album.
However, this is not his first "farewell" concert: the last one, which reunited him with Art Garfunkel, took place in 1993.
Tickets for BST are set to go on general sale on Friday.
