The 26-year-old forward joined the Hammers from Swansea on Tuesday in a deal believed to be worth around £20million.
The move sees Ayew reunited with his former Marseille team-mate Payet, who is now established as a firm fan favourite at West Ham after enjoying an impressive debut season.
Ghana international Ayew could go straight into the side to face Chelsea in their Premier League opener at Stamford Bridge on Monday night, with Bilic pleased to have him on board.
"He adds more quality," the West Ham boss said
"We had a really good season
Some people say it was unbelievable, most say it was a really, really good one
"So we didn't have the need to start from the bottom and change all the players although in football you are always trying to improve your team - and there are no yesterdays in football.
"He came to England and did a really good job
He scored 12 goals and played in different positions
He can be a game changer."
The record-breaking deal for Ayew continued a busy window of comings and goings for the Hammers, who are also looking to make the Europa League group stages by beating Romanian outfit Astra Giurgiu in a two-legged play-off.
As well as Ayew, Bilic has recruited Havard Nordtveit, Sofiane Feghouli, Gokhan Tore, Arthur Masuaku and Ashley Fletcher, as well as completing the permanent signing of Manuel Lanzini.
It has seen another injection of fresh talent into Bilic's squad - but it is Ayew who he has singled out for particular praise.
"We lost some players who were on loan to us - Victor Moses, Emmanuel Emenike, Alex Song - and one player that we didn't want to lose - James Tomkins - and we wanted to replace them with what we hope are better players," he added.
"And I'm sure Andre is one of them
He is a top player, he is a winner
He played for a long time at Marseille, where you have to be a strong character because the pressure is there 24/7 week in, week out, and he coped with that.
"And he wanted to come - you want players who want to come to West Ham.
"The players on our list were also on the list of clubs bigger than us and sometimes you have to convince a player to come here
But he was very excited and we are glad."
One of the reasons Ayew was keen to move from south Wales was to play with Payet.
"He's a friend of mine as we played two or three years together at Marseille," he told the club's official website.
"I know him and he knows me and I'm happy to be back playing with a great player like him, because I know what he is capable of doing.
And Bilic revealed he had spoken to Payet on a number of occasions when it came to his latest recruit.
"He was our target for a long time," said Bilic.
"But I did speak to Dimitri, two weeks ago and before in October or November and in March."
Source : PA
Source: PA