The jewel was mined last year in South Africa and cut and polished in New York in a six-month process.
Lau was convicted in Macau last year of corruption charges and received a five-year prison sentence. He remains free because Macau and Hong Kong have no extradition treaty. Lau did not personally attend the auction.
The sale price of the blue diamond also set a price-per-carat record, at $4,028,941 per carat.
Sotheby’s said Lau immediately renamed his prize The Blue Moon of Josephine in honor of his youngest daughter, 7. He also purchased a pink diamond for $28.5 million at the auction and said he intends to give both to his daughter.