The 32-year-old O'Donnell, who played in the Giants' season-opening win at St Helens a fortnight ago, becomes the Roosters' fourth close-season recruit, joining Sonny Bill Williams, James Maloney and Michael Jennings at Bondi Junction.
Roosters coach Trent Robinson, who witnessed O'Donnell's two injury-hit seasons in Super League as boss of Catalan Dragons, is delighted with his latest acquisition, saying: "Luke has plenty of experience, will fit into our system here well and we're looking forward to him starting."
He added: "Together with our other senior players in the forwards, he's sure to not only help on the field.
"It will be great to have him mentor the younger forwards we have coming through the ranks."
O'Donnell, who had 12 months left on his Huddersfield deal, said his desire to return to Australia with his young family was the main reason for his early departure.
"I'm looking forward to the challenge of playing in the NRL again and can't wait to meet my new team-mates and getting stuck into training," said the former North Queensland forward.