Coquelin, who is 29, makes the short move to Villarreal for a fee of around €6.5 million, plus €2m in add-ons.
"Villarreal and Valencia have reached an agreement for the transfer of Francis Coquelin," the club said on their website on Wednesday. "Welcome aboard the Yellow Submarine."
Meanwhile, 31-year-old Parejo also finalised his move from Valencia on a free transfer.
Recently appointed coach Unai Emery has made it his priority to strengthen the midfield after the departures of Santi Cazorla, Bruno Soriano and Zambo Anguissa this summer.
Cazorla has moved to Al-Sadd in Qatar, while Bruno has retired and Anguissa will be returning to Fulham after his loan ended.
Villarreal also wrapped up the loan signing of Japanese attacker Takefusa Kubo from Real Madrid this week.