Bacon, who died in 1992, aged 82, explained the gift in a recorded conversation with his friend Barry Joule.
UK newspaper The Sunday Times reported that Joule complied with Bacon's wish that the recordings should remain private for 12 years after his death.
Bacon reportedly met Capelo in 1988 when the banker was in his early thirties and the painter was 78.
"One has to think it's so abnormal of somebody of 35 like Jose having an affair with me. Do you see? I'm 40 years older than him," Bacon can be heard saying on the tape.
Capelo became a muse for Bacon, appearing in his famous 'Triptych 1991', which is on display at the New York Museum of Modern Art.
Another work, 'Portrait Of Jose Capelo' was put up for sale last year by a gallery in Switzerland.
In the conversation with Joule, Bacon refers to his sister, and says, “You see, I gave her exactly the same amount as I gave Jose.”
He adds: “Four million dollars. That’s over two million pounds, you know.”
It was apparently a decision that the artist had come to regret.
“I often think how stupid, what a fool I was to have done it,” he is heard saying. “And then I suddenly think, ‘Oh well, there it is, it is done’.”
Bacon's painting 'Three Studies of Of Lucien Freud' sold at auction last year for a record £86.6million.
Joule says that he will give the tapes to London's Tate Gallery to join the collection of 1,200 of Bacon's sketches that he has previously donated.
Capelo denied the veracity of the conversations but would not say specifically what he felt was untrue.
"I am not going to comment on what Mr Joule claims or says. I don't have that much respect for his opinion and his approach and his views," he told reporters.