Lyon striker Alexandre Lacazette underwent a medical at Arsenal on Tuesday with a view to a 44 million pounds ($56.91 million) move, British media reported.
The deal should be completed before Arsene Wenger's squad flies to Australia on Sunday and will be for a club-record fee, beating the 42.5 million pounds Arsenal paid Real Madrid for Mesut Ozil in 2013.
Lacazette's arrival is Wenger's first piece of significant business in the transfer window and follows the promise from chief-executive Ivan Gazidis last week that "top quality" summer signings would arrive this summer.
Arsenal are now likely to end their widely reported interest in Monaco striker Kylian Mbappe. Lacazette's signing could also mean the departure from Arsenal of another French international, Olivier Giroud, who struggled to hold down a first-team place last season.
For Lacazette, 26, the move to London represents a return to the ground where he began his professional career seven years ago, playing for Lyon against Celtic in an Emirates Cup match.
Since then he has developed into one of Europe's most prolific strikers, scoring 129 goals in 275 games for his hometown club.
Beginning his career as a winger, Lacazette has scored at least 22 goals each season since converting to a striker in 2013 and last season netted 37 times in 45 matches. His 28-goal Ligue 1 tally was bettered only by Edinson Cavan's 35 for Paris St-Germain.
Lacazette, who has won 11 caps for France, has spent his career playing under two of Wenger's protegees: Claude Puel, whom he managed at AS Monaco, and Remi Garde, who played under Wenger at Arsenal.
Lacazette is Arsenal's second signing this summer after Schalke left-back Sead Kolasinac, who arrived on a free transfer and trained with his new team mates for the first time at the club's London Colney complex on Tuesday.
FA Cup winners Arsenal play champions Chelsea in the Community Shield, the traditional curtain-raiser to the new season, on August 6.