Lacazette is understood to have become the Gunners' record transfer, with the fee understood to be in the region of £46 million.
The club confirmed the news on Wednesday, indicating that that the French striker has agreed a long-term contract with the north London outfit.
"Alexandre Lacazette has agreed to join us on a long-term contract, for an undisclosed fee," read a statement posted on the official Arsenal website.
"He is expected to travel with the tour party to Sydney this weekend and is likely to make his home debut in the Emirates Cup on July 29 or July 30.
"The deal is subject to the completion of regulatory processes."
The 26-year-old, who scored 37 goals in 45 appearances for Lyon last season, underwent a medical at London Colney on Tuesday, and eclipses Mesut Ozil - who cost £42.5m - as the most expensive purchase the Premier League club have made.
With hopes of signing Monaco's Kylian Mbappe - a Real Madrid and Paris Saint-Germain target - fading, Arsenal manager Arsene Wenger managed to convince another of Ligue 1's star forwards to play at the Emirates Stadium.
Lyon club president Jean-Michel Aulas, who sanctioned the transfer on Sunday, has previously said the Premier League side must part with €65m to prise Lacazette away from Parc Olympique Lyonnais and the newly agreed deal includes bonuses worth £6m.
France international Lacazette was close to joining Atletico Madrid before the Spanish club's transfer ban was upheld and Aulas confirmed via French news outlet Le Progres that Wenger's side that the move is closer to €50m (£44m/$57m) rather than an "unrealistic" €65m (£57m/$74m).