The 23-year-old was only able to make four appearances for the black, green and gold, all of which came from the bench during the 2019/20 season.
Uru began his senior career with Bury St Edmunds and made 38 appearances in National 2 South before attracting the attention of Saints in 2019.
But he was never able to establish himself in the first team, with Teimana Harrison regularly occupying the No.8 role.
Uru spent a successful spell with Bedford last season and has made nine appearances for the Blues so far.
Consequently, a switch to the Championship was the natural next step for the player, who has also previously had a loan spell at Nottingham.
And Bedford boss Mike Rayer said: "Tui is the first of many new signings for next season and we are delighted he will continue his development here at Goldington Road.
"We saw some exciting things from him throughout the shortened campaign and now, having sampled our environment and style of play, we think he’s going to flourish.”
Uru will now look to kick on as a full-time member of the Bedford team..
And he said: “I’m delighted to join Bedford Blues permanently, it’s a big benefit having been here last season and having got used to the environment.
"The coaches were really welcoming, I think I suit the style of rugby we play.
“We want to pick up from where we finished last season.
"The last game of the season against Ampthill was great, crowds returned to Goldington Road and that gave us a huge lift.
"I can’t wait to experience atmospheres like that again next season.”