Lloyd Embley, assistant editor of the Daily Mirror, which is also published by Trinity Mirror, has been appointed as acting editor of The People.
Gary Jones, head of news at the Daily Mirror, will assist Embley and The People's deputy editor Ben Proctor until a new editor for the Sunday paper is appointed.
Sly Bailey, chief executive of Trinity Mirror, said: "We thank Mark for his hard work and dedication. We wish him well for the future."
Thomas' departure follows the paper's fall below the 700,000 copy barrier in October, when it recorded a monthly average of 696,901, down 3.61% on September.
Its six-month average circulation figure was 727,248, down 12.17% from the previous year.
This was the worst performance of any Sunday newspaper, except the Sunday Sport.
Thomas started his career at The People, before becoming chief reporter at the News of the World, assistant editor on the Daily Mirror and then deputy editor of the Sunday Mirror.
He has been editor of The People since March 2003.
Thomas is the third Sunday editor to resign in recent months. Last month, The Observer announced that its editor Roger Alton would be stepping down in the new year, and Patience Wheatcroft resigned as editor of The Sunday Telegraph in September.