The attacking midfielder becomes the club's record signing and eighth signing of the season. He will wear the number 11 shirt, which was previously worn by Nikola Vlasic who is currently on loan at Torino.
The 25-year-old, who has also played for Flamengo and AC Milan, has been capped 33 times by Brazil and won the Copa América in 2019.
"I am extremely happy to be here. I hope it's the beginning of an enjoyable journey. I hope my time here is successful," the South American told the club's official website.
"Last season, West Ham had a very good season and I hope they continue to enjoy more and more good seasons in my time at the Club.
"I am excited to pull on the West Ham shirt and show the fans what I can do, to help my team-mates and the Club."
Meanwhile manager David Moyes hailed Paqueta's all-round qualities.
"I'm delighted to welcome Lucas to West Ham," said Moyes.
"He's a player I've admired from afar for a very long time and of course, we saw him close up in our Europa League campaign last season.
"He's a very talented footballer and whilst he will need time to adapt to the Premier League, we're excited about adding another proven international to our squad."
Earlier in the day rumours started by Lyon president Jean-Michel Aulas that another Premier League club had entered the race for the Brazilian midfielder's signature at the 11th hour turned out to be false, especially as Paqueta had undergone a medical at West Ham on Sunday afternoon.
"It's unfortunate that Lucas Paqueta is leaving. But he wanted to leave," he said.
"We thought we had very big clubs, we didn't have them. We had to talk at the last moment with West Ham.
"Now I know that there was an English club that wanted to come forward at the last moment so maybe tomorrow morning we'll wake up with a novelty. I can't tell you the name."
West Ham new signing Emerson, who played alongside Paqueta at Lyon, asked fans to be patient with the South American star.
"He has the talent to be one of the top players. He's still young and I believe we have to have patient with him, because sometimes youngsters have ups and downs," he said.
"He's a dedicated guy, someone who is obsessed with winning games and competing for titles. He has everything he needs to develop further. I think he has a brilliant future ahead of him."