The 24-year-old who plays on the right-wing scored an impressive 23 goals and produced 12 assists last season, driving Lillie to a second-place finish in Ligue 1.
Arsenal, who reportedly had a restricted budget this transfer window, will pay the large fee in installments, reports the BBC.
Napoli also had an offer accepted by Lille for Pepe, but the Ivory Coast international opted for the Premier League.
The transfer will be completed in the next 24 to 48 hours and will smash Arsenal's record for most expensive signing which currently stands at £56 million (A$100 million) for Pierre-Emerick Aubameyang.
The signing comes off the back of Arsenal completing deals for midfielder Dani Ceballos on loan from Real Madrid and 18-year-olds Gabriel Martinelli and William Saliba.
Pepe's price tag means that Arsenal are unlikely to continue pursuing Crystal Palace's Wilfried Zaha who they had bid £40 million (A$72 million) earlier this month. Palace valued Zaha at around £80 million (A$143 million).
Arsenal face Lyon on Monday morning (AEST) and will kick-off their Premier League season on August 11 against Newcastle.
