The player was tipped for big things upon his arrival at Arsenal but struggled to live up to expectations.
After leaving the club he spent a year in Turkey before becoming a free agent.
He will now be looking to make a major impact at Villarreal and prove that he can still play at a high level.
The winger joined Arsenal from Lille in 2019 for a then-club record £72million.
However, he endured a difficult time with the Gunners and left the club having made 112 appearances, during which he scored 27 goals.
Pepe had a loan spell at Nice before his Arsenal contract was terminated a year early by mutual consent.
Last season Pepe played for Trabzonspor, for whom he scored six goals in 23 games.
Nicolas Pepe, who spent last season at Trabzonspor, will hope to impress for Villarreal
Pepe recently revealed that he considered retiring due to the 'wave of criticism' that he received during his time at Arsenal.
In an interview with L'Equipe, Pepe said: 'It was almost harassment. I don't look at social media much, but if my brother told me "this is what they said about you", it would affect me unconsciously.
'It also came from the media or from certain members of the club. They don't realise that it can affect the mental state, the family and it affects performance.
'The only people who have always supported me are the Arsenal fans.
'At Arsenal, I suffered a kind of trauma, as if my passion had been ripped away from me, I had a disgust for football. I doubted myself to the point that I thought about quitting everything.
'I wondered how they could have been so relentless in their attacks on me. They even called me the biggest flop in the history of the Premier League. But I refused to mope.'