Moore will stay at Microsoft until Sept. 1, though Mattrick will start his new job on July 30.
The announcement comes two weeks after Microsoft said it would take a charge of up to $1.15 billion to fix an "unacceptable" number of broken Xbox 360 game consoles.
It also comes on the heels of E3, the video game industry's annual expo, where Moore had a highly visible role as host of Microsoft's press briefing. Microsoft said there was nothing to be read into the timing of Moore's departure.
"It's just how things fall. A lot of this timing was driven by Electronic Arts ," said Robbie Bach, president of Microsoft's entertainment and devices division that includes the Xbox 360.
"Peter's a sports nut, so it's a good job for Peter."
A month ago, EA's new chief executive, John Riccitiello, reorganized the publisher into four units to help make it more efficient.
As head of EA Sports, Moore will take charge of some of the company's biggest money-spinning franchises, such as "Madden" football, "FIFA" soccer and "Tiger Woods PGA Tour" golf.
"What I want to try to do is ... look at new ways to grow that business both domestically and internationally," Riccitiello told Reuters.
"Peter is an unbelievably talented executive. When he was running Sega and their sports business, it was the only time that EA felt threatened in sports," Riccitiello said.