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The club, which is based in Swansea, has signed Collins in a two-year deal.
He is expected to join the club at the end of the Super Rugby Trans-Tasman competition.
Collins has played for both the Blues and Highlanders in Super Rugby and also played for New Zealand under-20 in 2013.
Collins made his debut for Otago in 2012, his first year out of school at Otago Boys’ High School, and has gone on to play 71 times for Otago, scoring 17 tries. He started out as a midfield back but has played at fullback more recently.
He has captained Otago for the past three seasons and his wise head at the back will be greatly missed.
Collins, who qualifies for Wales through a Welsh grandfather, played in Wales with the Scarlets in the 2015-16 season.
Collins, who was born in Queenstown, said in a statement he had been sold on the plans for the club by coach Toby Booth.
"I spoke to Toby a while ago and this is a different challenge for me, one I have tasted before, and he just sold me on his plans for the team," he said.
“Having watched them from afar this season, the Ospreys are playing quite extravagant rugby and that is exciting too.
“I do have a Welsh qualification but for me, this is all about what I can do for the Ospreys and playing well for the Ospreys, and making a contribution to the team.
"With the PRO14 adding the South African teams, sides I have played against before, it will just add a whole new dynamic to that competition.”
Collins is also expected to be joined by Irishman Jack Regan at the Ospreys club.
The lock came out from Ireland last year to play for the Dunedin club and ended up playing for Otago in the national provincial championship. He turned out for the Highlanders earlier in the season, which has led to a contract at Ospreys.
As for who will replace Collins as the skipper of Otago it looks like hooker Liam Coltman, who has captained the side before, will take the armband again.