Media reports in East Yorkshire on Monday morning implied that the 23-year-old three-quarter had finally agreed a deal to leave FC.
It was also reported in 2014 that the player had gone to Newcastle RUFC for a trial in the other code.
Now, though, the Wildcats have snapped up the player on a deal which lasts until the end of the season.
“Joe’s experience will enable us to strengthen a position that we have been looking for more competition in all pre season,” said Trinity coach James Webster.
“We have been patient in that we needed to find a player that could really push for selection that was within what very small amount of budget we had left, and with him coming to a financial agreement with Hull allows us to do so.
“We have been able to pick up yet another player that is hungry but also extremely good value.”
He signed for Hull in time for the 2013 season, but struggled to hold down a first-team slot. He played 12 games on loan at Bradford in 2014.
“I am grateful to be able to get this opportunity to join Wakefield Wildcats,” said Arundel.
“Iit will allow me to focus on my game and improve to the standard I know I am capable of, but to also enjoy playing rugby again.”