The 20-year-old Cumbrian has been brought in to add strength to the Wildcats' pack and completed his first training session with his new team-mates on Wednesday ahead of the club's pre-season camp in Portugal next week.
Singleton has made one Super League appearance in each of the last two seasons at Headingley and played nine games for Dewsbury in 2012 to gain first-team experience.
"I've really enjoyed my first day and I think it's a very good club from what I've seen so far," said Singleton, who scored two tries in Leeds' 40-26 Boxing Day win over Wakefield.
"I need to be playing Super League because that's the next step of my career. I feel I'm ready and it's what I need to do for my own career to progress."
Singleton will join a big former Leeds contingent at the Rapid Solicitors Stadium along with Kyle Amor, Ali Lauitiiti, Lee Smith and Richard Mathers.
Wildcats coach Richard Agar said: "We needed to bring in one more prop to add some depth to that area of our squad and we are happy we have been able to bring in Brad.
"He is a young lad with a very bright future and he will certainly bring competition for places and will complement our pack."