Utility back Lilo starred in all four of Tonga's World Cup games including the defeat by England.
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.''