He made his Super League debut in 2015 and - with Tyler Randell having now left the club - will offer competition to fellow rake Kyle Wood.
Wood, 23, made just four appearances for Salford this season but is looking to get going again at Belle Vue.
"I had a disappointing year in 2019 due to a little niggle,” he said.
“But I've got it all sorted now and I'm ready for a fresh challenge in 2020.
"I feel like I'm ready to really kick on with my career now and I hope I can do that at Wakefield.
"When I've played against Wakefield in the past, it was always a tough game. As soon as I knew that they were interested, I thought it was a real good opportunity for me.
"I'm now excited for pre-season starting so I can meet all the lads and rip-in to the training."
Wood, who can also play in the halves, is Trinity's fifth signing of the off-season.
Chester said: “He's a tough player is Josh and a really nice kid.
"I'm looking forward to seeing him out there. He's got some decent deception at dummy-half. He's got a really good kicking game and for his size, he's a real tough defender.
"I think the balance between both nines (Kyle and Josh Wood) is just right.
“They're both clever out of dummy-half and both tough defenders. They're not the biggest of blokes but they like to get their bodies in front, which is what you want from a number nine."