The experienced Scotland second-row will drop down into the Championship with the relegated club on a one-year deal next season.
It is a significant capture for Leigh; Wardle, who played with Newcastle Knights in the NRL as recently as 2017, only turned 30 last month and has more than 200 career games to his name.
He only managed one match with Ian Watson’s Giants this season - a try-scoring appearance off the bench against Salford Red Devils in June - and had various issues with back, hamstring and calf problems.
But Wardle told The Yorkshire Post: “It was a bit annoying.
“I didn’t have a scan early enough on my hamstring until I’d done it three times.
“I couldn’t get going and everything seemed to go against me this year.
“I was pretty disappointed. When I was trying to find another club, it just puts everybody else off after what they have read.
“They’re scared. A lot were concerned with the injuries but if they’d actually dug deep they’d have realised I’m not as injury-prone as what was said to the press.
“The facts show I’m not that bad at all; the previous three years I’d not missed many games at all.
“I had to move on and try and get the best deal I could and, to be fair, I’m pretty happy with it at Leigh.
“I’m looking at this as a bit of a re-set and chance to get back playing again as well as it being a new challenge.”
Halifax-born Wardle started his career with Bradford Bulls in 2010 but moved to Huddersfield the following year and scored 62 tries in 141 games for Giants.
He was part of their side that lifted the League Leaders’ Shield in 2013 but four years later headed Down Under.
After a solitary season in the NRL, Wardle returned to Super League on a three-year deal with Castleford Tigers but returned to Huddersfield on loan in 2019 and made that switch permanent last year.
He has been impressed by Leigh after meeting their new head of rugby Chris Chester, the former Wakefield Trinity head coach.
“It’s full-time which is what I wanted - that’s one of the reasons why it appealed to me - and I still think I can go for another four or five years,” said Wardle.
“I was in talks with some Super League clubs but Leigh didn’t mess about.
“After speaking to Chris (Chester) and hearing his plans, and knowing what a passionate owner the club has in Derek Beaumont, it was all very appealing.
“I have played here in the past and the backing Leigh Centurions get from the fans is amazing.
“I am looking forward to playing here; we need to prove that we are the best in the Championship and get back into Super League.”
Chester said: “I have known Joe a long time.
“He is a good person, good trainer and will bring quality to the squad. He is a leader and will, I am sure, be a big asset both on the field and in the dressing room.
“He has plenty of experience both in Super League and the NRL who has bought into our vision at Leigh Centurions.”