The 24-year-old winger has been chased by Europe’s elite this summer.
Liverpool were sniffing around – along with Serie A side Napoli.
Pepe has scored an impressive 35 goals in 74 games during two years at Ligue 1 side Lille.
And, according to Gazzetta dello Sport journalist Nicolo Schira, the Gunners have now snared him.
“Unai Emery is closing in on Nicolas Pepe”
He posted on Twitter: “Done deal! #Arsenal have closed for Nicolas #Pepe.
“Gunners will pay him €80M to #Lille. Pepe will sign a contract until 2024 by €6M a year.”
Emery has also been chasing Celtic star Kieran Tierney.
However, the move looks deadlocked after the Scottish champions snubbed two bids.
Sky Sports reporter Kaveh Solhekol suggested last week that a deal is still uncertain.
“Still no third official bid yet but talks suggest all parties will be happy with the numbers when that is finally registered,” he said.
“Now that is a message that we got this afternoon, seeming to suggest that Arsenal are edging closer to signing Tierney.
“Good news you’d think for Arsenal supporters.
“We took that information and we put it to a source very, very close to Kieran Tierney to see if they would back that up.
“Unfortunately they came back to us with a very, very short message which was ‘not true at this time’.
“So we’re getting mixed messages about what is happening with Kieran Tierney.
“But through all the fog, I think we can say if Arsenal come up with £25m and structure that deal so it is more front-loaded, Celtic are willing to let him go.”
Arsenal could still offload players before the season starts.
Laurent Koscielny is widely expected to depart after refusing to join his team-mates on Arsenal’s pre-season tour.