Walker, 27, tested positive for cocaine following a game for Trinity at Widnes Vikings in July, 2017 and was suspended the following month.
He received a backdated 20-month ban in August last year and will be available to play again from March 14.
The Bradford-born Scotland internatioanl joined Trinity from St Helens on a two-year contract in May, 2017, but played only seven games games for them before the suspension which led to him leaving the club.
He said: “I’m absolutely thrilled to have a club for the 2019 season and I’m extremely grateful to Salford Red Devils for giving me this opportunity.
“From day one speaking to director of rugby and operations Ian Blease and head coach Ian Watson I could see that Salford – as a club – have some real strong beliefs and values that centre around the community and doing good in the local area.
“I knew straight away that this was the kind of club I wanted to be at.
“I’ve not been perfect in the past. I don’t think anyone is, but you need to learn from your mistakes and develop as a person and player afterwards.
“It’s been a tough few years for myself not being able to play the sport I love on a regular basis.
“I was suffering from some mental health issues at the time which in turn led to me making a big mistake.
“I don’t want to use that as an excuse, I accepted and learnt from my punishment.
“In my time away from the game I feel like I’ve matured a lot. I honestly feel I’ve turned the corner, I’ve regained my love for the sport back and I’m ready for the next chapter.”
Walker added: “At a club like Salford, I’ve got the best opportunity to continue to grow as a person by going into the community, talking about the lessons I’ve learnt and promoting rugby Llague in a positive manner.
“The sport of rugby league has been very good to me. The support I received from the RFL, in particular Emma Rosewarne, was brilliant and really helped me on my road to recovery.
“I’ve now been offered a second chance and it’s up to me to make sure I grab it with both hands.”
Reflecting on his past career, Walker recalled: “During my time at Hull Kingston Rovers I managed to draw attention from Australia and even spoke to Melbourne Storm, but I decided to see out my contract at Hull.
“Chris Chester [the ex-Hull KR and current Wakefield coach] was very supportive of me and that helped massively.
“I got the move to St Helens and then eventually Wakefield, both of whom are great Super League clubs.
“I was also in the Scotland national side on a regular basis and for that to slip away because of a silly decision whilst at Wakefield was massively disappointing, but it has only made me hungrier now to turn things around and strive to get back to where I want to be.”