The 27-year-old is expected to travel to France to undergo a medical after the two clubs agreed a deal which does not include an obligation or option to buy.
Pepe’s departure is a reflection of his minimal impact since making a club-record £72 million move from Lille in 2019.
The winger has scored 27 goals in 112 appearances but started just five games last season as manager Mikel Arteta preferred Bukayo Saka, Gabriel Martinelli and Emile Smith Rowe among others in Arsenal’s wide positions.
Pepe has two years remaining on his current contract and his situation will be reviewed next summer.
His exit will heighten speculation Arsenal could sign a winger before the end of the transfer window.