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The "ultra-rare" reference 2499/100 by the Swiss luxury watchmaker, one of only two cased in platinum, was acquired by Clapton some 10 years ago, it said.
It fetched a combined hammer price and commission that was in line with Christie's pre-sale estimate of 2.5-4.0 million francs while also setting a world record price for this reference at auction, it said in a statement on its semi-annual Geneva sale.
"The Eric Clapton watch was bought by an Asian private collector, " Christie's spokesman Cristiano de Lorenzo told Reuters, adding that the buyer had been in the room.
But the top lot at the seven-hour sale was another platinum chronograph Patek Philippe, reference 2458, made in 1952 for legendary American collector J.B. Champion. It fetched an early 3.78 million Swiss francs and set a world record for a watch without complications, or features beyond the display of hours, minutes and seconds, it said.
Precious Time, an investment watch fund launched by Luxembourg-based Elite Advisers, was the buyer, Christie's said in a statement.
In all, 96 percent of the 315 lots on offer found new owners, netting 27.04 million Swiss francs, the auction house owned by French billionaire Francois Pinault said.
Clapton's Patek Philippe, made in the Swiss city in 1987, has a perpetual calendar with moon phases, as well as windows for day and month and dials for seconds and minutes.
Most experts would rank it among the world's 10 most significant wristwatches that stand out for historical importance, mechanical complexity, beauty, original condition, rarity and superior provenance, Aurel Bacs, international head of Christie's watch department, said before conducting the sale.
Clapton, the former Cream musician, last year sold more than 70 of his guitars at a charity auction in New York, raising $US2.15 million for the Crossroads Centre drug and alcohol rehabilitation centre that he founded in Antigua.
Last month in London he sold an abstract painting by German artist Gerhard Richter at rival Sotheby's for $34.2 million, setting a record for the price paid at auction for the work of a living artist.
Antiquorum's sale of modern and vintage timepieces, held in Geneva on Sunday evening, netted 8.63 million Swiss francs for 485 lots sold out of 613 on offer, it said in a statement issued on Monday,
The top lot was a Rolex Single Red Prototype, known as the S ea D weller Submariner, o ne of only six produced in 1967 for use by divers. It sold for 490,900 Swiss francs -- four time its pre-sale estimate - in its first appearance at auction.
"It is the highest price ever paid for a Rolex sport watch and for a Sea Dweller," Antiquorum said.