The 28-year-old Brazilian joined the Hammers from Lyon in 2022 and made 139 appearances, scoring 23 goals and providing 15 assists.
Paqueta was given permission to fly to his home country earlier this week to make the permanent move before the transfer deadline on 2 February.
Paqueta, who had 18 months remaining on his Hammers contract, has played 18 times in the Premier League this season and scored four goals.
Despite not playing in recent matches Head Coach Nuno Espirito Santo said Paqueta will be missed. Santo Said: “For me, Lucas is a special player, a special person, he's a number 10 I think everything could be different, but the circumstances are what they are.”
"He wanted to go to Brazil, and you keep moving, knowing that he's special person and special player and we wish him all the best.”
Last summer, Paqueta was cleared of spot-fixing charges by an independent regulatory commission - almost two years after the Football Association launched an investigation into him.
He was facing the prospect of a lifetime ban if found guilty, but the regulatory commission found the four charges against him to be "not proven".
Paqueta is likely to be remembered fondly at West Ham, having helped them win the Europa Conference League under former manager David Moyes.