The transfer, worth a reported €25 million (£23m/$28m), is subject to a medical, while the Gunners also have first refusal on the midfielder.
Unai Emery's side are unlikely to bring him back to the Premier League, however, having signed the likes of Dani Ceballos on loan, Kieran Tierney from Celtic and Nicolas Pepe in a club-record deal this summer.
The 21-year-old left north London last summer after being told he was surplus to requirements by Emery, and went on to feature in 35 of Angers' 38 Ligue 1 matches in 2018-19.
Reine-Adelaide joined Arsenal in 2015 after progressing through the Lens youth system, but he was loaned out to Angers in January 2018 after making just eight senior appearances in three years at the club.
The Frenchman then made his move permanent last summer, and has since been called up to France's U-21 set-up.
His displays at the heart of the Angers midfield caught the attention of Lyon last season, and Les Gones have now agreed a deal in principle to sign the promising youngster.
Incidentally, his Arsenal career began in the pre-season Emirates Cup win against Lyon, in which his impressive display caught the eye.
He then had to wait until January 2016 to make his professional debut for the club, coming on as a late substitute in a home victory over Sunderland in the FA Cup.
He was also a key member of the Arsenal U-21 side that clinched promotion to the league’s first division in 2016.
Lyon kicked off their 2019-20 Ligue 1 campaign with a 3-0 away victory over Monaco, but manager Sylvinho is evidently still not satisfied with his squad.
The club's midfield was undoubtedly weakened after selling Tanguy Ndombele to Spurs earlier this summer, but Sylvinho is now looking to former Arsenal man Reine-Adelaide to fill that void.