The 27-year-old, who switched codes from rugby league in 2017, started all four of Fiji's pool matches at the Rugby World Cup in Japan, wreaking havoc in their tournament opener against Australia and scoring two tries in the win over Georgia.
"There is no doubt that Semi is one of the best players in the world, he's truly a world class performer and we are so excited about what he can do for the team," Bristol Director of Rugby Pat Lam said in a statement.
"Every top club across both codes on the planet wanted him, so for Bristol to be able to bring in a player of his quality underlines the fantastic work that the club is doing. As a person and a player, he is perfect for our culture which places an emphasis on community and high performance."
Radradra originally made his name in rugby league, scoring 82 tries in 94 games for the Parramatta Eels as well as representing both Fiji and Australia.
Lam told the club's website that Radradra really caught his eye when he coached the Barbarians against England last year.
"Everyone saw how he tore England apart that day (in a man of the match performance) with his ability but what I saw off the field (impressed me greatly)," he said.
"We all know the Barbarians is a lot relaxed but he put a lot of time and effort into preparation - unbelievably professional. While guys were doing touch he was doing his rehab and afterwards was doing extras and I just watched him.
"You can see the influence he had playing rugby league at a young age and starring for them and why he is so good because his whole preparation."
Radradra will join the Bears next year after completing his current contract with French side Bordeaux.
Pat Lam belives he can have a similar impact on the club to Fiji-born England number eight Nathan Hughes, who joined from Wasps in the off-season, and former All Blacks winger Charles Piutau.
Radradra adds to the already strong Pacific influence at Ashton Gate, with Manu Samoa internationals James and Jordan Lay, Chris Vui and Alapati Leiua, former Tonga captain Siale Piutau and ex All Blacks Piutau, John Afoa and Steven Luatua already on the books, under the tutelage of former All Black and Manu Samoa skipper Lam.
Bristol currently top the Premiership standings with 14 points after winning three and losing one of their four matches so far.