European champions Liverpool had a bid accepted for the winger though, but Pepe opted not to team up with Jurgen Klopp as the German couldn't offer him regular first team football.
Pepe's transfer beats the previous club record of £56 million for Pierre-Emerick Aubamyang.
Cote d'Ivoire winger Nicolas Pepe just completed his switch from LOSC Lille to Arsenal for a club-record fee of €80million. The length of the deal was not announced, but is believed to be for five years.
Speaking about his new signing, Unai Emery said: "Nicolas is a highly-rated and talented winger who was wanted by numerous top teams in Europe".
"He wanted to do a full season, he showed what he was able to do at home, in Ligue 1", he further added, about Pepe's campaign with Lille in the French League last season.
"Signing a top-class winger has been one of our key objectives in this transfer window and I'm delighted he's joining".
The £72million capture of Nicolas Pepe has rightly been received very well, but it would've been worrying if the club were willing to spend that money on the attack - arguably the team's strongest suit - rather than the defence.
With the transfer window for Premier League clubs closing on Thursday, Arsenal are rapidly running out of time to bring in defensive reinforcements.
"Also, Lacazette used to play for Lyon and so I have had the opportunity to play against him".
The Gunners disappointed last season when they finished fifth, meaning another year in the Europa League.