Although experts knew the works by the late painter existed, they had no idea who had bought them.
The artworks are titled Self-Portrait 1975 and Three Studies for Self-Portrait (1980).
A Bacon painting featuring his friend and fellow artist Lucian Freud, became the most expensive artwork ever sold at auction when it fetched $142m (£89m) in New York in 2013.
Oliver Barker, Sotheby’s senior international specialist in contemporary art, described the discovery of the portraits as “a pretty extraordinary collecting moment”.
“(Art dealer) Marlborough Fine Art kept a photographic archive and so both of these paintings appeared in a book on Bacon’s self-portraits, but apart from being reproduced in books they’ve not been seen,” he said.
“We knew of the existence of the paintings but simply had no idea where they could be. The first time I saw these paintings it was such a wonderful awakening. They’re both so luminous.”
Self-Portrait 1975 was painted at the height of Bacon’s career in the period which followed the suicide of his former lover George Dyer in 1971. Although Bacon was in his 60s he looked much younger in the work, having dyed his hair and worn make-up as he grew older.
Three Studies for Self-Portrait (1980) shows him with downcast eyes, increasingly haunted by the inevitability of death.
Mr Barker said that the artist “gave himself film star-style looks, appearing as photogenic as possible while still being highly self-critical”.
“He paints himself with a much more youthful appearance,” he said.