Monaghan, 28, was sacked by the Raiders for an off the field incident following the end of the season, and he has since been seeking a move to Super League.
He will join up with brother Michael at the Halliwell Jones Stadium, while the club has also confirmed that double Challenge Cup winner Hicks has retired.
Head coach Tony Smith said: “We are delighted to be signing Joel as players of his calibre does not become available too often and the timing of this opportunity along with Chris Hicks reconsidering his retirement has meant it has all fallen into place for the best interests of all concerned.
Joel is a player we have considered signing in the past and its fair to say that the chance has come along sooner than expected, but we also feel that it is absolutely the right time to stand by and support Joel and his brother Michael, and this will certainly enhance our squad for the season ahead.”
“I personally would really like to thank Chris for his services over the past three seasons, everybody here at the club has thoroughly enjoyed working with him.
Both on and off the field Chris has always acted like a true professional, he has left many happy memories and will do for years to come.”
Hicks, 33, signed for the club from Manly for the 2008 season and scored 71 tries and 144 goals in 82 games for the Wolves.
He said: “I see this opportunity as a good time to reconsider my retirement since realising that this move for Joel could be on the cards, It’s helped make the descision that much easier knowing that there will be a sound replacement stepping into the club. Ive been friends with both Mick and Joel for a while and the chance for them to play together will be a great move for the club.
“Also many thanks to the club for giving me three great years, epecially thanks go out to the fans and our friends at the club for always making us welcome and feel at home.
“I have made lots of friends and take away nothing but fond memories, Warrington will always be close to my heart.”