Moore, an experienced halfback, was ever-present in Fax’s side in 2015.
“This is the first time that I have enjoyed my rugby in years,” said the 27-year-old.
“We have a tight bond at Halifax and we all agreed that it was far from a successful season last time out, and we are now focused more than ever to make sure the Club gets back into the top four in 2017.”
Robinson, also a halfback, joined Fax from Hull KR in 2015, and played 14 times last season, scoring seven tries.
“I would have liked to been involved a lot more last year,” he said.
“Hopefully now that I have signed a new contract, I can hit the ground running in pre-season and give the gaffer something to think about ahead of the new season.
“There are exciting times ahead at Halifax and I am very pleased to be a part of this club.”