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The figure is made up of auction sales, which saw their biggest increase ever, up 88% to $4.3bn, and private sales, up 5% to $494.5m. Christie's auction sales rose by a more modest 34% to $4.4bn, the significant gap between the two for 2009 all but closing.

It means that private sales, made away from the glare of the saleroom spotlight, now account for just over 10% of all sales at both Sotheby's and Christie's.

The latter announced a 39% rise in private sales for the year, giving a sterling total of £369.3m, broadly equivalent to about $560m.

It also means that the world's two leading auctioneers are now among the world's leading dealers in terms of turnover.

Sotheby's turnover was $774.3m, with profits of $161m – the company's best year after a record 2007. Of the profit, $96.2m came from the fourth quarter.

Just as the staggered buyer's premium protects the auctioneers' revenues in a falling market, so it acts as an attractive marketing incentive as prices rise. This certainly appeared to be the case in 2010, when there was a 105% increase in the number of works sold over $1m, the point at which the buyer's premium rate decreases from 20% to 12%.

"The recovery of the global art market, which was aided in part by the increased buying activity of clients from new markets, certainly contributed to these results," said Sotheby's chief executive Bill Ruprecht, "as did the difficult decisions we had to make beginning in the autumn of 2008 – the headcount reduction, tightening of our cost structure and steadfast focus on auction commission margins.

"Our success was achieved with a much lower risk profile than in the previous peak years of 2006 and 2007, as we have been highly selective in our use of auction guarantees and only issued such guarantees in tandem with risk sharing arrangements that very significantly reduced our financial exposure," he continued.

The significant upturn has allowed Sotheby's to reduce their debt obligations, and Mr Ruprecht revealed that sales for the first two months of 2011 were already ahead of the equivalent period for 2010.

Sotheby's have not yet published separate figures relating to their online bidding service Bid Now, which they launched last year. Their rivals' equivalent, Christie's Live, is a much more established operation, and Christie's were keen to highlight that 28% of all their clients now bid via the internet on Christie's Live, accounting for 11% of all sales at £76m – a rise of 69% on the total taken in 2009.

Christie's also reported that new clients registering to bid rose by 22.7%, with new buyers up 13%.