The winger is due to fly into London for his medical on Tuesday, and will sign a five-year deal worth £138,000 a week.
Gunners manager Unai Emery is accelerating his spending with less than two weeks to go before the start of the new Premier League season.
Arsenal are also expected to make a third bid for Celtic defender Kieran Tierney as they attempt to strengthen a defence that showed as many weaknesses as ever in the 2-1 defeat by Lyon in the Emirates Cup at the weekend.
Ivory Coast international Pepe, 24, was also being chased by Napoli, but the winger has opted for a move to the Premier League.
Arsenal have turned to the Lille star, who scored 22 goals last season and provided 11 assists as his side finished runners up to Paris Saint-Germain in League 1, instead of Crystal Palace forward Wilfried Zaha.
Arsenal did so because the French club did not want the whole fee, which would have been similar, paid up front, but instead in instalments.
The Gunners will hand over £20m upon the deal being completed, with the following £52m being split over the next four years, Lille receiving £13m per year.
Pepe’s wage demands were also understood to be lower than those of Zaha, who is now in limbo having angled for a move away from Palace.
Celtic value highly rated full-back Tierney, 22, at around £30m, and Arsenal are expected to increase their last offer of around £25m this week.
Confidence of the prospect of landing the Scottish international is increasing among Emirates chiefs, despite deadline day rapidly approaching.
Tierney made 40 appearances for Celtic last season before a hernia injury interrupted his campaign.
Pepe will become Arsenal’s fourth signing of the transfer window, following the purchases of Gabriel Martinelli and William Saliba – who will remain on loan at Saint Etienne – and the loan arrival of Dani Ceballos from Real Madrid.
More good news for the Gunners on Monday night came as it was learned that striker Alexandre Lacazette has only sprained an ankle and is expected to be fit for their opening league game of the season against Newcastle.
The striker will though miss Arsenal’s final two warm up games, against Angers on Wednesday and Barcelona on Sunday.
Lacazette has struck up a strong partnership with Pierre-Emerick Aubameyang since the Gabon international’s arrival from Borussia Dortmund last January.
And Emery will be hoping Arsenal’s latest big-money acquisition, Pepe, gels quickly with the prolific duo as Arsenal plot a return to the top four.