Ellis, 22, was released by Hull earlier this week, enabling him to make the move to the PROBIZ Coliseum, where he had already signed a deal for the 2013 season.
Australian McGoldrick, who has been with the Tigers since 2006, has handed in a transfer request, which has been granted. The utility back has not been offered a new deal for next season, and is expected to sign for another Super League club.
Coach Ian Millward said: “Ryan approached us out of the blue about leaving. Although as a senior player we’d ideally have him leading us from the front for the rest of the season, with him out of contract we have reluctantly accepted his transfer request.
“With Ryan being a player that has given seven years of service to this club it would be wrong to deny him of this opportunity to continue his Super League career beyond the current season. He leaves with our best wishes for the future.
“Ryan’s departure enables Jamie Ellis to come in early. We have struggled with our kicking game this year and Jamie gives us a quality kicking game.”
Ellis goes straight in to contention for Sunday’s clash against Huddersfield, as the Tigers look to bounce back from Monday’s 40-10 defeat at the hands of Widnes.