The 24-year-old, who can also play at full-back, moved to the Recreation Ground from London Irish at the start of last season.
Watson was part of the England squad that toured New Zealand earlier this summer, though he is yet to make his Test debut for his country.
"Anthony is an incredible talent and we're obviously delighted he's staying with us," Bath head coach Mike Ford told the club's official website.
"I think what is most exciting for us as coaches is that he's still young and still has so much potential to get better. He has a real natural ability on the field and that will only become more finely tuned as he gets more experience."
Bath got their new Aviva Premiership campaign off to a winning start last Saturday with a 29-20 victory at Sale Sharks.