The 24-year-old Queenslander has played 37 games for the Rabbitohs in three seasons and scored 16 tries, including a hat-trick against the Roosters in 2009.
While Simpson scored nine tries in 18 appearances that year, he managed just eight matches last season, scoring just twice.
Following the arrival late last year of Kangaroos and Maroons centre Greg Inglis, Simpson requested he be released early from his contract which had little under a year to run.
Simpson said: “I’m really looking forward to heading to the Huddersfield Giants and starting the next phase of my football career.
“It’s a great opportunity for me to play rugby league in other countries and experience the rest of world.
“I’m grateful to the Rabbitohs for the opportunities they’ve given me over the past three seasons both on and off the field.
“I wish my team-mates, the coaching staff and the club the best of luck for this year and for the seasons to come.”
Souths chief executive Shane Richardson said the club did not want to stand in Simpson’s way.
“Jamie has an opportunity to head to the UK with Huddersfield and play in the elite rugby league competition in Europe,” Richardson said.
“This is a great opportunity for Jamie to take up a contract in the English Super League and also explore a bit of the world whilst playing rugby league. We wish him the best of luck in his move to England.”
Simpson has signed a three-year contract and will fill the void created by the departure of former New Zealand international Paul Whatuira.
Giants head coach Nathan Brown said: “It’s great news for us and ends the search for the outside back that we have talked about for some time now, which brings more balance and experience to the squad.
“Jamie is primarily a centre/wing which will help take some pressure off our crop of exciting younger backs who have had excellent pre-seasons which has pleased all the coaches.
“Jamie has always scored tries throughout his career and, at 24, he has his best years in front of him.”
Simpson must now await a visa, which means he is unlikely to arrive in time for the start of the new season on Feb 12, and in the meantime he will continue to train with Souths.
He is Huddersfield’s second major recruit for 2011 following the capture of North Queensland forward Luke O’Donnell.
Hull KR prop Rhys Lovegrove is expected to miss the first month of the new season after suffering knee ligament damage.
The 23-year-old suffered the injury in training this week, but does not require surgery.
His absence leaves coach Justin Morgan light on front-row forwards, with his major off-season capture Willie Mason yet to arrive in the country.
The former Australia international is still awaiting the arrival of his visa and the club have not been able to confirm when he will land in England, so rookie forward Richard Beaumont will get the chance to push his claims for a place, starting in Sunday’s friendly at Huddersfield.
Harlequins RL have named former Zimbabwe international cricketer Gus Mackay as their new chief executive.
Mackay, who made three limited-overs appearances for Zimbabwe, has held a similar position with Sussex County Cricket Club, while he has also had management roles with both Surrey and Leicestershire.
He replaces Paul Blanchard, who has left the club to work for the Surrey Sports Park.
“I am looking forward to joining Harlequins Rugby League,” said Mackay.
“I am aware of the significant challenges which we face with this sport in London. However, I am confident that we can make a real impact and build on the good work and strong base which exists.”
