Biggs, who was born in Hull, had been rumoured to be considering a move North last month but Bath initially suggested they were keen to keep the former England Saxons star in the West Country.
The invitation to embrace a new opportunity in his native city proved too good to turn down, though, and Biggs will change codes in the summer.
"Hull FC approached me and I'm very excited to have the chance to try my hand at league, and especially with my local club," said Biggs.
"I've thoroughly enjoyed the last few seasons here at Bath, and am genuinely sad to be leaving. The supporters and everyone involved with the Club have been fantastic whilst I've been here, and I've been lucky to work with some great coaches and players. I've no doubt that the current squad will continue to develop over the next couple of years into a very exciting side.
"Now that the decision has been made, my focus is totally on Bath and making sure that I do all I can to help us continue our good start to the season."
Biggs currently has more than 80 Bath appearances to his name ahead of Saturday's Amlin Challenge Cup opener at Bordeaux-Begles.
A Powergen Cup winner with Leeds in 2005, Biggs has scored 24 tries for Bath since joining from Newcastle Falcons in 2010.
"Tom has been a huge asset to Bath Rugby whilst he's been here, and a complete professional on and off the field," said Bath director of rugby Gary Gold.
"We'll miss his commitment and skill in matches and training, and his dry sense of humour! We're obviously sad to be losing him, but this is a fantastic opportunity for Biggsy and we wish him the very best of luck."