Piutau, who played 17 Tests for New Zealand between 2013 and 2015, said he loved the All Blacks jersey and what it stood for.
"But when it comes to a place when you can provide for your family and there's a better opportunity, to me it was an easy decision. I'll always choose my family over anything else.
"I'm so thankful for everything that happened in New Zealand, but as well as wanting to provide for my family, I also wanted to experience this side of the world."
Piutau will join his older brother Siale at Bristol, who are coached by former Blues mentor Pat Lam.
The younger Piutau has also taken a place on the players' board of Pacific Rugby Players' Welfare, the organisation to further the aims and interests of Pacific Islanders based in Europe.
"Joining PRPW is a chance for me hopefully to give back to the Pacific Islands community in a small way," he said.
"For players to know they have a support network and a voice when playing in Europe, I think that's important."
- AAP