The self-portraits are going on public display for the first time after being rediscovered in a private collection, before being sold.
Although experts knew the works by the late Irish-born British painter existed, they had no idea who had bought them.
The paintings are expected to fetch up to 15 million each when they go on sale at Sotheby's London Contemporary Art Evening Sale in July, BBC reported.
The artworks are titled Self-Portrait 1975 and Three Studies for Self-Portrait (1980).
"(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," Barker said.
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.
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