The 28-year-old completed a club record transfer fee reportedly worth £18 million on Wednesday, penning a three-and-a-half-year deal.
He joined the club together with Andy King, who made a loan switch from Leicester City.
“We have signed two players and the most important thing is that they are two players who really wanted to come here,” said, Carvalhal.
"When I spoke to Andre, he said to me ‘I want to go to Swansea’. It was the same when I spoke to Andy.
“They wanted it a lot and this is crucial because we want players who want to be here with us.
“If you bring in a player with quality who does not want to be here, it’s absolutely sure that he wouldn’t help the team.
“But when you have two players with qualities that can help the team like Andre and Andy and who want to come, you will be stronger.
“It’s not just about quality, it’s about commitment. This is the biggest thing for me.
"Both Andy and Andre are team-workers, which is important.
“The reason why we have done well in the last few weeks is because we are a team, not because we have one or two stars. The new players will add to that.”
But Ayew's signing was more refreshing for the Jack Army.
During his first spell in 2015-16, the attacker netted 12 goals in 34 league outings, finishing the season as the club's top scorer.
He then joined West Ham after just one season at Liberty Stadium.
"Andre is a good solution for us,” Carvalhal said.
"He is very versatile and can play in different positions. He is not exactly a No. 10, but he does not lose the ball easily and this kind of player can link the midfield to attack.
“At the same time he is a threat because he scores goals.”
Ayew, who made 18 league appearances involving nine starts and three goals for West Ham this season before his transfer, could make his debut for Swansea in Saturday's topflight trip to Leicester.