Paqueta has signed a five-year contract with the option to extend for another season at the London Stadium.
West Ham have now made eight summer signings, also bringing in Alphonse Areola, Flynn Downes, Nayef Aguerd, Gianluca Scamacca, Maxwel Cornet, Thilo Kehrer and Emerson Palmieri.
Paqueta spent the last two seasons with Lyon, having joined from AC Milan in the summer of 2020.
The 24-year-old scored 18 goals in 67 Ligue 1 appearances for Lyon, adding a further 11 assists.
Speaking to West Ham's official website on his arrival at the club, Paqueta said: "I am extremely happy to be here. I hope it's the beginning of an enjoyable journey. I hope my time here is successful.
"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."
West Ham manager David Moyes added: "I'm delighted to welcome Lucas to West Ham. 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."
Paqueta has won 33 caps for Brazil, scoring seven goals and was part of their 2019 Copa America winning squad.
