The Tonga international, 26, has joined on a two year deal and is the West Yorkshire club's latest addition ahead of 2022.
It is the second time Giants coach Ian Watson has signed him after bringing him to Salford from Leeds Rhinos in 2019.
"We know what Tui is good at - he's good at running the football and breaking into open space," he said, with Lolohea having helped Red Devils to their first-ever Grand Final two years ago and Wembley last season.
"He's got unbelievable footwork. He's also a strong boy; if you get him in open space, there's not too many that can stop him.
"I've worked with him for a couple of years, I trust him and what he does.
"We've built a great relationship and we're good at working together to get the results we want.
"When he gets his eyes up and plays off the cuff, he's a great player to have in our side."
The ex-New Zealand Warriors and Wests Tigers star said: "I know Ian Watson and his philosophy and what he wants from the team.
"I'm looking forward to the new challenge and seeing what I can do here.
"I'm close with him; we text and talk and I'm looking forward to winning games and trying to get some silverware with this club.
"He wants leadership first and foremost, there's a lot of young players coming through so trying to help them and build their game.
"I'm looking forward to working with (conditioner) Greg Brown as well; him and Ian have a good balance in their qualities and I'm looking forward to being around them again.
"I try and play off the cuff, take opportunities and play with the flow. I'm looking to build my game around different things but improve myself while I'm here."
Huddersfield stand-off Lee Gaskell has joined Wakefield Trinity for 2022 while captain and scrum-half Aidan Sezer has joined Leeds so Giants have been in the market for a half-back with St Helens' Theo Fages also expected to join youngsters Will Pryce and Olly Russell at John Smith's Stadium.
Watson has also signed England prop Chris Hill from Warrington Wolves for 2022, Leigh Centurions prop Nathan Mason and brought back Seb Ikahihifo from a two year loan stint at Salford.
Salford director of rugby and operations Ian Blease added: "Tui has been exceptional during the two years he was a Red Devil, playing a massive role in helping the club achieve back-to-back major final appearances.
"He came to us during a tough time in his career, but has shone throughout his stint with us and it's safe to say his game has definitely improved.
"We wish Tui and his family all the best for the future."