Goal revealed in January that the 16-year-old and international team-mate Kelechi Nwakali were due to join the Gunners early in 2016.
The pair have since been pictured at the club's training ground, and now Chukwueze has confirmed he is on his way back to London to join Nwakali, who is understood to have made the trip two weeks ago.
"My trip to London is on Monday night," Chukwueze told AfricanFootball.com. "I'm happy that everything is going well and I will do my best when I get there by the grace of God."
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Chukwueze also revealed the reasons behind his decision to move to Arsenal.
He added: "Arsenal as you well know are a very good club and it will be good for my career since I will be able to learn many new things.
"I like Arsenal because they are a club who give young players the opportunity to showcase their talents and I believe I would be given the chance to play too."
Chukwueze and Nwakali caught the eye as part of Nigeria's Under-17 World Cup-winning side in Chile in 2015.
Both players will not be eligible to sign professional contracts with the Gunners until their 18th birthdays.