Ayew rejoined the Swans two seasons ago from West Ham United, but went to Turkish side Fernabache on a season-long loan, before returning to the Championship side after his loan spell.
He decided to stay with Swansea and has been one of their best performers.
Cooper who is impressed with his leadership qualities has made him the deputy skipper of his team with immediate effect.
“Andre is a senior figure and a very positive influence around the group,” said Cooper.
“We are very lucky, we have players like Wayne Routledge, Nathan Dyer and Kyle Naughton too.
Steve Cooper and Andre Ayew
“We know there is a bit of a status to being captain or vice-captain, but we do have senior figures in the squad.
“Andre has got the attributes to lead, and he does it well through good and bad moments and long may that continue.
“It’s good for Matt as well to have players like Andre, Wayne and Nathan around him.
“Matt has thrived in the role, there is no doubt about it. But I know he is open-minded enough to seek advice and I know those boys will give it to him in a constructive and helpful manner.
“Andre is a good role model and leader, I think there is a good culture here everyone helps each other but pushes each other. That’s a good thing.”
Andre Ayew was appointed captain of the Black Stars few weeks to the start of the 2019 Africa Cup of Nations (AFCON) after Asamoah Gyan was stripped of his captaincy duties for the senior national male football team.