The Kiwi will be one of the highest paid players in the world.
Bristol say they faced “massive competition” before securing the services of New Zealand star Charles Piutau.
Piutau will move to the west country next year after his existing contract expires with Guinness PRO14 side Ulster.
The former Wasps back is among the most sought-after players in world rugby, and his signing represents a major coup for Bristol.
Press Association Sport understands, though, that Bristol refute a reported £1million per season salary for Piutau.
New Zealand World Cup winner Dan Carter is currently thought to be rugby union’s highest-paid player on a reported 1.2m euros (£1.1m) yearly deal at French Top 14 club Racing 92.
Bristol were relegated from the Aviva Premiership in May, but they are hot favourites to win the Championship this season and reclaim top-flight status.
“Charles is one of the best rugby players in the world – he has proved that over the years,” Bristol’s chief operations officer Mark Tainton told Bristol Rugby TV.
“When he played for the (Auckland) Blues he was averaging 1.5 tries a game, which shows what kind of quality he has got.
“There were many clubs around the world trying to get his signature and we are pleased he has come to us.
“He has looked at what we are trying to do and he believes in what we are trying to do, and he wants to add to that.
“There was massive competition. It didn’t happen overnight. It was a long process – many phone calls, many conversations – but we are delighted he has come in.”
Ulster, meanwhile, have adopted a philosophical stance to Piutau’s move.
“It is disappointing that Charles is moving on,” Ulster operation director Bryn Cunningham told the province’s official website.
“But salaries for the world’s best players are rising year-on-year and are ultimately determined by what one club is prepared to pay for an individual.
“We have a strong commercial programme in place and that has allowed us to attract top overseas players and to retain our best home-grown talent in what is a hugely-competitive market.
“Our strategy is to continue to recruit world-class players in the seasons ahead.
“Charles is a fantastic player who delivered many match-winning contributions in his first season with us, and I’m sure he will produce plenty more over the next 10 months.
“I know that he remains committed to helping us reach our potential in both the Guinness PRO14 and (European) Champions Cup.”