Bristol chief executive David White said: "This is a significant signing for Bristol and we are looking forward to David joining us on November 1 following the conclusion of the New Zealand NPC competition.
"He is an experienced, well-performed player who has the ability to play both fly-half and inside centre."
Bristol head coach Richard Hill added: "We have been closely following David Hill over the last 18 months and have been impressed with his progress, in particular his leadership in the pivotal fly-half position, his accurate goal-kicking, flair and versatility.
"Having spoken to David at length, we believe that his attitude and character will be a real asset to the squad. At only 27 years of age, he is at his prime and will be integral to the continued development of Bristol Rugby."