Lawson was overlooked for The Daily Telegraph editorship when the job went to Martin Newland following Charles Moore's retirement in 2003.
His resignation comes a year after the £665m handover of The Telegraph Group from Hollinger International to the Barclay brothers, which prompted the redundancies of 90 journalists across the Daily and Sunday titles and high-profile commercial departures including managing director Hugo Drayton.
Lawson has kept a low profile in comparison with other national newspaper editors, but he attracted attention after the Asian tsunami disaster with a front-page Sunday Telegraph article implying that the disaster had led the Archbishop of Canterbury, Dr Rowan Williams, to question God's existence.
Lawson, who was on holiday on the day of publication, subsequently wrote to apologise to the Archbishop for the front page, which was done in his absence.
Sands takes over at The Sunday Telegraph as its six-month average circulation is down 1.57% year-on-year to 689,617. She has been deputy editor of The Daily Telegraph since 1996 and in 2004 was given responsibility for editing the Saturday edition of The Daily Telegraph.
Prior to joining The Daily Telegraph, she was features editor and associate editor of the Evening Standard.
Murdoch MacLennan, the chief executive of the Telegraph Group, said: "Sarah will be responsible for reviewing the style and content of The Sunday Telegraph and its supplements. Alongside Martin Newland, she has done a first class job on the daily, boosting the sales of the Saturday edition. I have no doubt she will bring a new and different approach to the Sunday market, " MacClennan said.
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