He said: "After 10 years at Independent News & Media I have decided it is time for me to move on and seek new challenges. I would like to thank my brilliant staff for their tireless dedication and support, and I am immensely proud of our achievements together.
"I am particularly proud of our campaigns for the rights of the mentally ill and, most recently, for the honouring of the Military Covenant and better treatment of British troops in Afghanistan and Iraq."
Davies led the redesign of the IoS during summer last year, when it was slimmed down to one newspaper section and one magazine.
He first joined The Independent soon after it launched in 1986 and worked his way up, eventually replacing Janet Street-Porter as editor of the IoS in 2001.
John Mullin, deputy editor of the IoS, takes over temporarily from Davies as acting editor.
Ivan Fallon, chief executive of Independent News and Media UK, said: "We shall miss Tristan, who has been the longest serving editor of the Independent on Sunday.
"He has established the title as an innovative, pioneering and campaigning paper, with a record of breaking stories and setting the Sunday agenda."
Separately, Sir Anthony O'Reilly, the chief executive of IN&M, increased his personal stake in the company yesterday to 26.6%. He spent €2.3m (£1.7m) to buy another million shares at €2.33 a share.
The move comes a day after his rival, Irish businessman Denis O'Brien, increased his stake in the business from 15.4% to 16.4%.
O'Brien, who has been calling for INM to sell The Independent and Independent on Sunday, is viewed as a "dissident shareholder" by O'Reilly, who has vowed to resist any calls to sell off the titles.