The 26-year-old, who scored his 65th try in his 123rd game for the in Sunday's 68-16 club-record Super League win over Leigh, has signed a two-year contract with Glasgow.
It's a return to his rugby roots for O'Hare, who made his name in the 15-a-side code as a Wales Under 21 international. He played union for New Brighton and Leeds Tykes before switching to League with the Leeds Rhinos.
In his five years at the Giants he has become a firm favourite with the fans.
But Huddersfield general manager Richard Thewlis admitted the offer O'Hare received was too good for him to refuse.
"Because of Hefin's background, rugby union clubs have always kept a very close eye on him," said Thewlis to the Huddersfield Daily Examiner.
"And Glasgow must have been extremely impressed with what they have seen, because they have come up with a fantastic offer which is impossible to refuse.
"Hefin has also made no secret of his desire to play European Cup rugby at some stage of his career, and that's what Glasgow can offer him.
"He has kept us fully informed throughout his talks with Glasgow and he goes with our full blessing.
"He's been an outstanding player for Huddersfield Giants over the years and we wish him well for the future."
Glasgow backs coach Sean Lineen said: "Hefin is a very clever player with a mature head on broad shoulders. With the departure of Sean Lamont, Rory Kerr, Kenny Logan and other three-quarters over the summer, we needed to look carefully for suitable replacements. This lad fits the bill.
"He has played union at a decent level and anyone with a scoring record like his in Superleague is no slouch."