The Ghanaian winger became the East London club's most expensive signing when he joined from Swansea City for £20.5million earlier this week and is now eager to link up with former Marseille mate Payet under the guidance of Slaven Bilic.
"We have a very good relationship, he's a friend," said Ayew.
"I'm happy to be in the same squad as him. He's a great player, he has great quality.
"I'm not surprised with what he did last season because I even know he is going to do more this season, he has the quality to do more.
"With him, and all the other guys who have come in, with (Sofiane) Feghouli, I had to take my time, have a discussion with the manager, he made me understand what he wanted."
Ayew added: "I knew that this club is a very popular club, has a lot of ambitions, wants to get to another level and I want to be part of that project."