The pair will be supported by Aaron Heremaia and Tom Gilmore as vice-captains.
Widnes coach Denis Betts said: “Widnes Vikings has strong leadership qualities across the team, so I canvassed the views of our players and coaches in making this decision.
“I am delighted that the Club will be led in 2017 by our leadership group of Chris and Joe, supported by Tom and Aaron.”
“The Leadership Group has great character, lots of understanding and are inspirational in their actions.
“We have a fantastic team of players who want to work hard, enjoy being here and aspire for success. I’m excited for the season ahead.”
Co-Captain Mellor said: “It’s an honour to be named as one of the four leaders for the upcoming season.
“I’m very proud to have been selected for this role by the coaches and my teammates. We know what it will mean to the town if we can bring greater success to the Club and that is something that really motivates us all.”
Co-Captain Houston said: “I’m delighted to have been named as one of the Co-Captains for the upcoming season, with Joe.
“I have been involved in leadership roles throughout my career and I am looking forward to building on this experience at Widnes Vikings.
“I want to lead by example – playing and training well, and always giving it my all. The Club has some outstanding young players and I’m looking forward to supporting them.”