Sidoli was a key member of Wales' 2005 Grand Slam-winning team, having made his Test debut against South Africa three years earlier.
But he is not currently part of the Wales squad, and his move to Bristol comes as the west country outfit prepare for second-row Sean Hohneck's departure to Italian club Viadana.
Utility back Lilo played in all four of Tonga's games during the 2007 World Cup, including their final pool fixture against England in Paris.
Bristol head coach Richard Hill said: "We've been talking to Robert for some time now, and he will certainly boost our second-row resources for next season.
"I was impressed with Robert's desire to be part of what we are trying to achieve at Bristol.
"We've also kept an eye on Vunga since the World Cup last year, when he was one of Tonga's star performers.
"He's had a really good season down at the Cornish Pirates, and he will give us options at centre and full-back."
Bristol lock Nathan Budgett, meanwhile, has signed a new one-year deal at the Memorial Stadium.