Met chiefs branded his behaviour as unacceptable and moved quickly to limit the damage from the episode.
Scott is alleged to have greeted the demise of Thatcher, saying her death was "87 years too late" and writing that the world was a "better place".
Commander Allan Gibson said: "This officer's behaviour was completely unacceptable and it is right he has resigned.
"The officer chose to resign immediately prior to his suspension being put in place."
In a statement the Met added: "The officer concerned today submitted his resignation and it was accepted with immediate effect."
The Met said the officer served in an operational support role and had reported himself to the force's directorate of professional standards on Wednesday, after the story broke. Scott's alleged tweets were published by the Mail on Thursday evening.
In reaction to so-called death parties that greeted the former prime minister's death on Monday, Scott reportedly tweeted: "Marvellous stuff!Margaret Thatcher's death greeted with street parties in Brixton and Glasgow."
He attacked other politicians, allegedly posting: "Goodnight Twitter. The world is a better place today now that c*** is dead. Now for Cameron, May and Osborne."
The Scott case comes as figures show 38 claims have been substantiated against Met officers over their use of social media.