Gallagher is a former England Under-20 international, and was on the team which won the World Rugby Under-20 Championship in 2016. He began his career at Saracens and joined Bath in 2022 after a two-year spell at Munster.
The full-back, who has scored eight tries in 35 appearances with Bath, has signed a three-year deal with the Italian club, and his contract will begin on July 1.
"Benetton Rugby has done very well in recent seasons and Italian rugby is growing really well," Gallagher said.
Gallagher, who can also play wing, qualifies to play for Italy through his mother's family and is also eligible for England, Ireland and New Zealand. He is the son of John Gallagher, who won the 1987 Rugby World Cup with New Zealand.
"Benetton has a great rugby history and is building something big in Treviso. In addition, my grandparents live in Trentino and this means that I will be able to see them more, which my family will appreciate very much," Gallagher added.
The signing comes just days after another former England Under-20 player, Louis Lynagh, was confirmed as joining the Italian club from Harlequins. Lynagh received his first call-up to the Italy squad on Wednesday before they play France in the Six Nations.
Benetton players make up 16 of the current 33-man squad, with another three players out injured. Gallagher's move to the club will almost certainly result in him being named by head coach Gonzalo Quesada in one of his upcoming squads.
