Addo-Carr will join the club at the end of the season in a deal that will see him wear the purple jersey until the end of 2019.
The 20-year-old winger has played four NRL games for the Tigers, scoring three tries and made his NRL debut against Storm in Round 7 of this season.
"I'd like to make it clear to our members and fans that Wests Tigers made a very competitive offer to retain Joshua for the next few years and while we're disappointed we wish him well," Wests Tigers CEO Justin Pascoe said.
Wests Tigers also confirmed Asipeli Fine has been granted an immediate release from the remainder of his contract. Fine played three NRL games for the Tigers since making his debut in Round 25 of the 2014 season.