The Gunners had an initial bid for the 26-year-old France international rejected, but talks continued.
His fee, of up to £52m with add-ons, will surpass the £42.4m Arsenal paid Real Madrid for Mesut Ozil in 2013.
Lacazette was second top scorer in Ligue 1 – the French top flight – last season with 28 goals.
He has scored 129 goals in 275 matches in all competitions since breaking into the first team in the 2009-10 campaign.
His league tally last season was bettered by only Paris St-Germain’s Edinson Cavani, with 35.
Lacazette, who has won 11 caps for France, has been linked with several top clubs and looked set to join Atletico Madrid before their transfer ban was upheld by the Court of Arbitration for Sport.
Last week Arsenal chief executive Ivan Gazidis promised fans “top-quality” summer signings during a question-and-answer session.
Left-back Sead Kolasinac, who joined from Schalke, is Arsenal’s only recruit since the end of last season.