Ford, 23, turned professional with Leicester having joined the Tigers as a 16-year-old, but left for Bath in 2013.
"This hasn't been an easy decision for me to make, but I feel it is the best one for me at this time," Ford said on Tuesday.
"I've really enjoyed my time at Bath and have worked with some incredible players and coaches."
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Ford developed as an exciting playmaker at Bath under the tutelage of his father, Head Coach Mike, but had been linked with a move ever since the club sacked the senior Ford last May.
Bath-born Burns started out with his hometown club before joining Gloucester's academy, turning professional in 2009. He joined Leicester at the end of the 2013-14 season.
The 26-year-old says he is eager to return home.
"The opportunity for me to represent my hometown club is one I have dreamt of from the day I started playing rugby," he said.
"I am looking forward to working under (director of rugby) Todd Blackadder and being part of a young and ambitious team to bring more success to the club.
"You can see they are building something really exciting in the way they are playing... It will be great to be part of that."
Burns made his full international debut in 2012 and has won five caps.
Ford, who made the breakthrough a year later, is firmly established as England's first choice at Number 10, making 33 appearances, most recently in Saturday's Six Nations victory over Wales.
(Editing by Mark Trevelyan and John Stonestreet)
