The presenter will host a new BBC1 sports programme next summer, and will also work at Five Live.
Logan cited ITV's decision to give Steve Rider the World Cup presenting role as a major factor in her career choice, saying: "I interviewed David Beckham but I didn't see a single game. It dented my confidence and made me question my abilities. If you've got ambition it's obviously disappointing."
"I'm thrilled to be joining the BBC at such an exciting time," she added. "The opportunity was one I just couldn't resist."