RNZ reports the 25-year-old Blues player is expected to leave after the Super Rugby season.
Luatua has played 15 Tests for the All Blacks, debuting in 2013 and playing his most recent game against Italy on the 2016 end-of-year tour.
He will link up with his former Blues coach Pat Lam at Bristol.
"The signing of Steven - beating off competition from a number of high profile clubs - underlines the ambition of Bristol as well as Stephen Lansdown and the board's desire to drive us forward," head coach Mark Tainton told website bristolrugby.co.uk.
"Since bursting onto the scene as a 19-year-old, Steven has been a consistently formidable presence, both at Super Rugby and for the All Blacks.
"He's a hungry, ambitious 25-year-old and a standout performer at the very highest level - we're delighted to welcome him to Bristol and it's a massive acquisition for us."
Luatua, who can also play in the second row, has made over 60 Super Rugby appearances for the Blues.
The player said: "I have a fantastic relationship with Pat [Lam] and I enjoyed working with him at the Blues. I'm looking forward to taking on a new challenge with Bristol and contributing to the long term vision of the club.
"Bristol is one of the most ambitious clubs in the UK and that's backed up by a really passionate fan base. I've heard great things about the environment that is being built there and the plans in place, so I can't wait to get started in the summer."