The 23-year-old winger had already agreed a contract to join the Giants in 2017.
Wire head of coaching and rugby Tony Smith wished Ormsby well in the next stage of his career.
“We are delighted for Gene,” he said.
“He probably wasn’t going to get too many more chances here with us over the next little while – having a few people playing in his position – so the opportunity was there for him to start at his new club.
“He’s very grateful for the opportunities he’s been given here at Warrington and I’m sure he’ll express that himself.
“We are also grateful for the contributions he’s made; it’s been great to watch his development as a player and a person over a number of years.
“This is the right thing for him to go. He needs to play more regularly and I think he’ll be able to do that at Huddersfield.”