Arundell, who will become eligible to play for England again on his return to the Premiership, has scored seven tries in his international career so far, including a joint-record of five in a single match on his World Cup debut against Chile in September 2023.
He began his career in London Irish’s academy, and went on to score 10 tries in 23 senior appearances for the side before the club folded at the end of the 2022-23 campaign.
“Henry has some world-class attributes, more specifically his speed and try-scoring ability,” Bath head of rugby Johann van Graan said.
“Henry made it very clear when we spoke that he wants to improve as a player and I believe that Bath is the club to do that.
“His willingness to learn, grow and become better fits in well with what we, as a group of players, coaches and staff are all working towards on our journey together.”
Arundell becomes the second high-profile signing for Bath for next season in the space of two days, with Gloucester and Argentina full-back Santiago Carreras having also agreed terms to move to the Recreation Ground.
The current Premiership league leaders have also signed hooker Dan Frost from Exeter and scrum-half Bernard van der Linde from South African side Bulls.
Additionally, England centre Ollie Lawrence has recently agreed new terms to stay at the club, along with prop Beno Obano and second row Quinn Roux.