According to the Telegraph, Bristol saw off strong competition from leading clubs in France to secure the deal - well beyond Ulster's financial means - and had to pay above the odds because of their current status outside of England's top flight.
Bristol, who were relegated from the Premiership last season, had already set a new Premiership record by signing Piutau's former Auckland Blues and All Blacks team-mate Steven Lautau this season on a deal understood to be worth £650,000 per season.
Former Blues coach and director of rugby at Bristol Pat Lam said the signing of Piutau was "one of the biggest coups in the club's history".
"I feel blessed to have been given the opportunities I have in rugby," Piatau told the Telegraph.
"If I am able to play a central role in delivering the vision that Pat has outlined for Bristol, then the challenge of playing for this club will be an achievement that I will be able to look back on, with immense pride.
"Even more appealing, is the opportunity to do this along side my brother Siale, my best friend Steven (Luatua) and the rest of the squad that Bristol is putting together."