The Gunners will pay £20 million ($24.5 millon) of that record £72 million ($88 million) fee upfront.
The remaining portion of the fee will be paid over five years and the Ivorian is set for a medical by the end of the week.
The signing will be an impressive coup for the Gunners hierarchy given Paris Saint-Germain, Manchester United and Napoli have all been credited with an interest.
The 24-year-old Pepe will form part of what should be an exciting forward line next season
Pierre-Emerick Aubameyang and Alexandre Lacazette scored 50 goals between them last season and Pepe will add to manager Unai Emery’s firepower.
He was second only to PSG’s Kylian Mbappe in the Ligue 1 scoring charts last season, registering 22 goals and 11 assists as Lille finished second.
And Arsenal’s spending may not stop there. The club still have a keen interest in Celtic left back Kieran Tierney and are after a centre half.
Meanwhile, Lacazette expects to be fit for the start of the Premier League season at Newcastle on Sunday week despite suffering a sprained ankle in Arsenal’s defeat against Lyon last Sunday.