The Rams also confirmed a link-up earlier this week with League 1 outfit Hemel Stags.
“It is a good opportunity for my fringe players to be playing every week,” Chester told reporters.
“Dewsbury’s on our doorstep and we are going to get the use of some of their facilities as well. It is a step in the right direction.
“I am more than happy with the arrangement.”
Trinity will also play a preseason game against Rams next year, with the Championship club set to keep the proceeds.
Dewsbury chairman Mark Sawyer believes that the new partnership is positive news for both clubs.
“The decision to enter into a playing partnership with Wakefield Wildcats has been taken after careful consideration, with the conclusion being that it is in the best interests of the club,” he said.