ESPN reported that Arsenal were close to agreeing a deal to sign the 21-year-old midfielder last month.
Lokonga made his senior debut for Anderlecht in 2017 after coming through the club's youth academy and made his breakthrough in the 2019-20 campaign with 26 appearances in all competitions.
He established himself as a regular under manager Vincent Kompany last season and featured 37 times across all competitions, also chipping in with three goals and three assists.
"Albert is a very intelligent player who has shown great maturity in his performances during his development," Arsenal manager Mikel Arteta said. "He has been coached well by Vincent Kompany and his team at Anderlecht. I know Vincent very well and he talks so highly about Albert and the positive impact he had to Anderlecht in recent seasons.
"We're confident Albert's ready for the next stage in his development and we're looking forward to welcoming a new member to our squad with his quality and presence."
Arteta is keen on strengthening his midfield options this summer with Dani Ceballos now back at Real Madrid, Granit Xhaka in negotiations to join Roma and s Lucas Torreira available for transfer. Meanwhile, Matteo Guendouzi has left to join Marseille.
Sources told ESPN the Gunners had scouted Lokonga for some time, dating back to before the start of the coronavirus pandemic.
Lokonga has been capped seven times at Under-21 level for Belgium and received a call-up to Roberto Martinez's senior side in March but was an unused substitute.
He is Arsenal's second signing of the summer following the arrival of defender Nuno Tavares from Benfica this month.
Arsenal finished eighth in the Premier League last season and will begin their 2021-22 campaign at newly promoted Brentford on Aug. 13