The 19-year-old, who was released by West Brom last week, has signed a two-year deal at Prenton Park and Parry claims he will be the first of many new arrivals.
"He is strong, likes to get forward and I'm delighted he is our first signing of the summer," said Parry.
"He fits in really well to the way we want to play and I'm pleased he has decided to come back permanently.
"To be able to bring in a young player of this calibre shows the club's commitment to improving the squad and Joss is just the first of many new faces we want to bring to Tranmere this summer."
Labadie Career Factfile
Born in Croydon, Labadie started his football career with West Bromwich Albion, joining their academy in 2006 after being spotted playing for Barking Abbey College of Sport and being invited for a trial. In the 2007/08 season, he played 19 times for Albion's reserve team, scoring three times. It earned him his first professional contract in the summer of 2008, on a one-year deal with the option of a second season.
Before he was able to break into the Albion first team, he was sent on loan to League Two side Shrewsbury Town in January 2009. He played his only game for Shrewsbury in their league game with Bradford City at Valley Parade, in a game which finished 0–0, before his loan spell was ended after he fractured his foot in training.
He returned to Shrewsbury on an initial month-long loan on 3 August. He made his first appearance of the 2009/10 season in a 3–1 victory over Burton Albion, during which he scored a free kick from 30 yards. He returned to West Brom in November, with Shrewsbury manager Paul Simpson saying "I've been disappointed with his recent attitude". Later the same year, he had another loan spell in League Two, this time with Cheltenham Town.
In March 2010, Labadie signed for Tranmere on loan until the end of 2009/10 season. He made his club debut during a 3–0 defeat to Brighton & Hove Albion.