Christie's chief executive Steven Murphy will leave the auction house by the end of the year, the London-based company announced on Tuesday.

The move comes just over a week after Sotheby's executive and chairman William Ruprecht announced he was stepping down. Both Murphy and Ruprecht said their departures were by "mutual agreement" with the companies although the Sotheby's head came under fire from activist investor Daniel Loeb.

Murphy will be replaced by Patricia Barbizet who will continue as chairman. French luxury goods billionaire François Pinault owns Christie's.

"When Mr Pinault and Madame Barbizet brought me into Christie's, I was tasked with helping to modernise the company and enable it to grow in the new world in which we operate, while maintaining its extraordinary spirit and culture, and consistently focusing on the art itself. We have now successfully concluded an ambitious three year plan and the company is in the strongest leadership position in its history," Murphy said.

Named CEO in 2010, Murphy did not disclose plans for the future other than spending time with family.