Christies has agreed a settlement in principle with Mr Dickson and his sister
Christie's has reached an out of court settlement after selling a painting for £8,000 which turned out to be a lost original Titian worth up to £4m.
Its previous owners had accused the auction house of negligence over the sale of the picture - Salome with the Head of St John the Baptist - in 1994.
The painting was put up for sale last year by Sotheby's with a guide price of $4m to $6m.
Christie's agreed the settlement at the High Court in London.
The painting was unearthed in the family home of David Seton Pollok-Morris Dickson and his sister Susan Marjorie Glencorse Preistley.
Mr Dickson, from Symington, Ayrshire, and Mrs Preistley, from Clapham, south London, sued Christie's, claiming breach of duty by staff who had examined and researched the painting before its first sale.
They claimed Christie's had failed in its commitment to competently "research and advise" on the painting's value.
They also said they were told by Christie's that cleaning the painting would be an unnecessary expense, but that, had cleaning been carried out, the true nature of the picture would have been discovered before the 1994 sale.
It was sold in December 1994 for the £8,000 reserve put on it by the auction house.
In 2001 the painting passed into the hands of Milan-based private collector, Luigi Koelliker, who hailed it as a lost Titian masterpiece, once belonging to King Charles I.
It subsequently featured in major exhibitions of Titian's work in Edinburgh in 2004 and in Vienna and Venice in 2007 and 2008.
Last January the painting was put up for auction as part of Mr Koelliker's collection, with a guide price of $4m to $6m.
The trial was due to begin at the High Court in London on Wednesday before Mr Justice Eady, with Christie's expected to contest the siblings' claim.
However, after negotiations at the doors of the court, the case was adjourned, with the parties having agreed a settlement in principle.
If a settlement is agreed, it is likely to be finalised on paper without another open court hearing. The terms of any deal will be kept confidential.