Wardle, 25, will play under ex-Giants coach Nathan Brown at his new club.
He was part of the team that won the 2013 League Leaders' Shield and played more than 100 Super League games.
Australian utility back Mamo, 22, is recovering from a broken ankle but expects to link up with the Giants by the middle of January.
Mamo told BBC Radio Leeds: "I'm excited by the change as I have only ever lived in Australia. I will give it my all.
"Hopefully I will play full-back and that's what I've spoken to (Giants coach) Rick Stone about.
"I have known Rick since as I was 18 at Newcastle and I have had a good relationship with him. He has always helped me out a lot and he was one of the reasons when I re-signed at Newcastle initially."
Mamo suffered his injury when he was hit by a motorcycle while on holiday in Bali.
"I had to come home and have surgery but I am on the mend at the moment," he added.
Huddersfield Giants have signed Jake Mamo on a two-year deal from Newcastle Knights, with centre Joe Wardle moving the other way on a three-year contract.