The diamond sold after five minutes of bidding
It was graded as "fancy vivid" - the highest level of colour intensity.
The rectangular-cut stone was found in a South African mine around 100 years ago and has likely not been altered since it was first cut in 1920, Christie's said.
Finding a fancy vivid pink diamond larger than 10 carats is virtually unheard of, the auction house said.
The auction price of the Pink Legacy diamond, sold at Christie's annual Magnificent Jewels auction, beat the previous record price-per-carat.
In November 2017, an 8.41-carat pink diamond sold for $17,768,041 (£11,438,714) in Hong Kong - more than $2.1m (£1.8m) a carat.