Monaghan, 33, is entering his seventh season with the club, whilst Westwood, 32, celebrated his testimonial year last season.
Head coach Tony Smith is confident the pair will work well together.
“Both are very highly respected players within our group,” said Smith.
“They both bring something a little different to the table in terms of leadership, and do it in different ways, but I think they complement each other very well.
“It’s an opportunity for both of them to lead the way and share some of their experiences and wisdom within our group.
Smith also added that there will be other players called upon to lead the Wolves during the season.
“We are making them our club captains but it doesn’t necessarily mean that they will be our on-field captains on a weekly basis,” he explained.
“We have a number of candidates who may fill that role at different stages, but they are certainly seen as our two ambassadors and role models for the younger people within the club.”