Regarded as one for the future by Ronald Koeman, he is expected to be loaned out to Anderlecht in the 2016/17 season to continue his development in Belgium.
Onyekuru, who scored 22 goals in 38 games in the Belgian Super League this past season, caught the eye of the Gunners as the club had reportedly agreed a £6.8m ($8.7m) deal for the forward towards the end of May.
Onyekuru confirmed the bid shortly afterwards, revealing his excitement at the prospect of joining the north London club, having been a fan of Arsenal legend Thierry Henry as a youngster.
"It's a good feeling for a club like Arsenal [to] come to make an offer for me -- this is due to my hard work in training and games. It's a good feeling," Onyekuru said. "I am waiting and working towards it and we'll see how it goes after the [Nigeria] qualifiers."
"Thierry Henry has always been my idol since I was a kid. I love watching him play, watching Arsenal and going to YouTube to watch most of his games.
"I remember saying if I had to move to the Premier League I want to be like Thierry Henry, so it's like a dream come true and I'm looking towards it at the moment."
However, Arsenal were not the only club interested in his services as Onyekuru issued an ultimatum earlier this month that first team football was of the highest priority for him.