The Gunners have spent the past 48 hours locked in talks with Pepe’s representatives after agreeing a £72 million deal ($87m) with Lille for the 24-year-old attacker.
There are a few minor details still to be ironed out between both sides, but Pepe is scheduled to travel to England from France later today to put the finishing touches on his move and undergo his medical.
He will then sign a five-year deal which will see him earn around £150,000 per week, with Arsenal hopeful he will be fit enough to play some sort of part in their opening Premier League fixture of the season at Newcastle on August 11.
The Gunners are in action in France on Wednesday night when they take on Angers and they complete their pre-season campaign with a game against Barcelona at the Camp Nou on Sunday.
Arsenal will fly into Spain on the day of the game and it's too early to say whether Unai Emery will consider handing Pepe some minutes against the Liga champions.
Speaking about the prospect of the Ivory Coast international arriving, Arsenal's head coach said: "We are working, the club, and also thinking about how we can improve.
"There are different players on the table with the possibility that we can achieve their signature.
"Pepe is a very good player and also we are thinking only of players who can really, really improve this squad and also give us some different conditions to improve.
"We have been working for the last few weeks and before we start the season in the first match against Newcastle, our aim is to get the best team with the best players in our squad."
He predominantly plays on the right side of the attack, although he can operate on the left or as a striker.
Arsenal will pay Lille around £20m ($24m) up front, before paying off what remains of the fee in a series of instalments over the length of his five-year contract.
Fonte, who played with Pepe last season at Lille, said: "He is incredible. If he can reach the same level, which I believe he will, that he did with Lille last season then Arsenal fans will be very happy.
"He is super quick, he has a left foot which is silky, one vs one he is second to none. He finishes really good, he takes penalties, he takes free-kicks.
"He is a very, very accomplished player and I think Arsenal fans will be in for a treat, for sure."
Pepe will be Arsenal’s fourth signing of the summer following the additions of Gabriel Martinelli, Dani Ceballos and William Saliba, who will spend the coming season back on loan at Saint-Etienne.
The Gunners will look to finally secure the signature of Celtic left-back Kieran Tierney once Pepe’s move has been confirmed.
The Scottish side have rejected two bids for Tierney already this summer, but Arsenal are expected to return with a third offer in the coming days which they hope will see them given permission to open talks with the player.