The news was announced by Millwall Football Club earlier today with former boss Colin Lee moving upstairs to become Director of Football.
The 33-year-old former player, who was appointed assistant manager to Lee earlier in the season, becomes the youngest manager in The Championship and the fourth Lions boss in little over eight months, following the departures of Dennis Wise and Steve Claridge.
The reshuffle followed a meeting between De Savary, chief executive Ken Brown, director Constantine Gonticas, Tuttle and Lee, although there had been rumours at Saturday's game against Reading that changes were afoot.
"It was a surprise, but the position excites me and I have a stack of work to do," said Lee.
"There is a clear understanding that David will keep the job for the rest of the season - and if he keeps Millwall in the Championship I'm sure he would keep the job.
"David is a young man, and the chairman wanted to give him a chance. I'm a perfectionist who finds it difficult to relax at certain times, whereas David is more laid-back. The players support the decision fully."
Tuttle's first game as manager will be the Boxing Day clash against Leicester City.