Snitch, 26, has signed a three-year deal with the Tigers.
The move to The Jungle marks the end of Snitch’s second spell with the Wildcats.
“I’m looking forward to joining the Tigers and working with Terry,” said Snitch. “Cas have improved a lot this year and have some really good players and some top youngsters in the squad.
“I know a lot of the guys at Cas from my Huddersfield days so it should be easy to settle in.
“There is no reason why the club can’t go even better next year and I’m hoping that I can add something to the pack.
“Generally I play in the back row but I’m happy at prop, the main thing for me is being out there on the pitch.
“In the immediate future, though, I have a job to do at Wakefield and I’ll be giving them my all until the end of the season.”
Castleford coach Terry Matterson was pleased with the signing, saying, “We do need to add some particular strengths and I feel that Steve will prove a top acquisition for the squad.
“As well as in the second row he can also do a job up front and he has had a great season this year.”