"He gives you composure, he creates opportunities and space for other players."
The Ghana international won the BBC African Player of the Year in 2011 and signs a four-year deal to become West Ham's record signing.
"Ayew has a thigh injury, he told me it's not a big one but you never know," Bilic said. "He will have a scan and we have to wait for the result of the scan to know how long he will be out."
The Hammers will qualify for the Europa League group stage if they beat Romanian champions Astra Giurgiu over two legs, starting in Giurgiu on Thursday
The Ghana forward has signed a three-year deal with a two-year option and becomes the club's ninth summer signing.
“We wanted to get into the Europa League and it was a reward for last season,” said Bilic. “There is big hype about qualifying for the Europa League. Everyone at the club wants to participate. It is a great experience for the players to participate in different countries.”
The former Liverpool full-back signed a one-year deal on a free after being released by Real Madrid at the end of last season
"Four months is a big, big blow for us but we have to cope with it."
"He was our target for a long time," Bilic said. "But I did speak to Dimitri, two weeks ago and before in October or November and in March."
The Hammers' head of medical Stijn Vandenbroucke said: "Andre underwent a scan and the medical team will now assess the results with a leading consultant before drawing any conclusions.
"It is not good and he needs surgery," said manager Slaven Bilic after his side's 1-1 Europa League qualifying draw against Astra Giurgiu.
"I spoke to him yesterday, he felt good and he looks good in training, but he's not ready yet for 90 minutes. It was the plan to bring him on. He gives you composure, he creates opportunities and space for other players."
"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."
"Feghouli picked up something against Juventus which we didn't think was an injury and he trained for a week but he is injured," said Bilic.
"Ayew has a thigh injury, he told me it's not a big one but you never know," said Bilic.
The Romanian team knocked West Ham out a year ago, after coming from two goals behind at Upton Park to earn a 2-2 draw, before capitalising with a 2-1 win at home a week later.
Sofiane Feghouli, Havard Nordtveit and Ashley Fletcher signed on free transfers from Valencia, Borussia Monchengladbach and Manchester United respectively.
Swansea have already strengthened their attacking options by bringing in Fernando Llorente, while Atletico Madrid's Borja Baston is also on their radar.
Despite the injury problems in attack, Bilic insists he will not rush Dimitri Payet back into action after his exploits with France at Euro 2016.
The Hammers’ £20m record signing suffered a thigh injury on his debut against Chelsea on Monday night and limped off less than half an hour into the 2-1 defeat.
"He will be out for 4 months. Good luck Andre."
Slaven Bilic believes West Ham's club-record signing Andre Ayew can be a "game changer" and consulted with Dimitri Payet about the striker before completing the deal.
It has seen another injection of fresh talent into Bilic's squad -- but it is Ayew who he has singled out for particular praise.
"I want to train hard, do my job and show that I deserve to play for West Ham United. I want to give back to the manager and the fans the confidence they are showing me."
Ayew, 26, signed for Swansea on a free transfer from Marseille in June 2015 and scored 12 goals in his first Premier League season.
Sofiane Feghouli is also struggling with a hamstring injury, while Dimitri Payet will continue to be eased back into action after starting on the bench at Stamford Bridge.
The £20.5million signing from Swansea made his debut for West Ham at Stamford Bridge but pulled up after just half an hour as he chased Eden Hazard.
Ayew, André - West Ham (ENG)
"The club have a lot of ambition and have a great manager," said Ayew.
“For me they played a good game against Copenhagen at home and I know how good the teams from Romania can be.”
"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."
"I spoke to him yesterday, he felt good and he looks good in training, but he's not ready yet for 90 minutes. It was the plan to bring him on.
"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.
Ayew spent just one season at Swansea following a move from Marseille, where Hammers star Dimitri Payet was among his team-mates.
The fee is £20.5m, according to West Ham's co-chairman David Gold, eclipsing the £15m the club paid Liverpool for Andy Carroll.
This game at the Stadionul Marin Anastasovici is the filler of three matches sandwiched into six days – and the Premier League matches against Chelsea and Bournemouth are very much the bread-and-butter.
Following the 2-1 defeat at Stamford Bridge on Monday night, Bilic will be keen to make the first league match at the new London Stadium a successful one, while making no secret of the poisoned chalice that regular Europa League football – the reward for winning this two-legged play-off – represents.
"He has suffered a significant injury and it is imperative that we do not rush to conclusions and we receive the correct diagnosis by consulting top specialists.
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.
And Bilic revealed he had spoken to Payet on a number of occasions when it came to his latest recruit.
Manuel Lanzini was also left in London after suffering a knee injury while preparing for the Rio Olympics football tournament with Argentina, but Bilic is confident he will return to action in just one week – albeit a busy one.