"Aurel Bacs, the Senior Consultant, Phillips in Association with Bacs & Russo has dubbed the watch the "'Adam and Eve' of the watch collecting world". The timepiece sold to an anonymous bidder on the phone after 12 minutes of spirited bidding.
Newman wore the mechanical watch in the late 1960s and 1970 when he began racing cars under the moniker P.L. Newman, according to the Washington Post.
Cox made a decision to sell the piece, in part, to raise money for the Nell Newman Foundation, where he serves as treasurer.
The auction house described Newman's Rolex, which the actor is said to have worn every day between 1969 and 1984, as "arguably the most iconic collector's wristwatch of the 20th century".
The word "DAYTONA" appears in red above the middle subdial.
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Newman gave the watch to a James Cox, a former boyfriend of his daughter Nell in the 1980s. I replied, 'I don't know - I don't have a watch.' He was clearly surprised.
"Paul asked me what time it was, to set his watch", Cox told The Wall Street Journal. "If you wind it, it tells pretty good time".
"At that time, I knew Rolex was an wonderful brand, but I had no idea how significant the watch was".
She had engraved "Drive Carefully, Me" on the caseback.
Eventually the watch was sold for $17.8 million, making it about $6 million more expensive than the previous most expensive watch ever sold at auction, Business Insider noted. Before Thursday, the most expensive Rolex ever sold at auction was the Bao Dai - a yellow gold, automatic style - that fetched $5 million at Phillips in May.
Newman died September 26, 2008, at age 83.