Dawai (29) will join the side at the conclusion of Otago’s season and has penned a two-year contract with the Irish outfit.
Connacht won the Pro 12 league last year and is coached by former Blues coach Pat Lam.
Otago coach Cory Brown used to work for the Connacht side.
Dawai said in a statement he was excited to be joining the club and making his next move in his rugby career.
Born in Fiji he moved to Southland before making his Southland debut in 2013.
He moved north the following year and made his Otago debut in 2014.
Last year he was impressive, scoring a hat trick for Otago at Eden Park and ended up scoring seven tries in the season.
This year he has been hampered by an ankle injury and did not play a lot for his club team, Harbour.
He can play all three loose forward positions but appears to be at his best on the blindside flank.
He will play for Otago tonight at No 8 against Manawatu.
Lam said in a statement he was excited to be having a player like Dawai to come to the club.
"We were really impressed with the rugby Naulia’s been playing in the NPC and also with the Fiji national side during the summer. When Cory Brown confirmed to me Naulia’s work ethic and ability on and off the field, we were very pleased to secure him for Connacht Rugby," Lam said.
Other New Zealanders playing for Connacht include former Blues hooker Tom McCartney and Chiefs midfielder Bundee Aki.