The 25-year-old has marked a five-year contract with a further one-year choice and will wear the No 14 shirt for the Hammers.
Cornet finished his clinical on Friday prior to settling individual terms to become David Moyes' fifth significant summer marking following Gianluca Scamacca (£35.5m), Nayef Aguerd (£30m), Alphonse Areola (£10.5m) and Flynn Downes (£12m).
At first, it was thought West Ham's inclination was a credit, yet the club were ready to meet Cornet's delivery statement.
"It's another step for me to join this huge club and I'm truly glad to be here, to be essential for the venture for the club. I'm simply eager to begin," he said.
"Everybody realizes the level here in the Premier League is exceptionally high and I need to play here for that, so I'm truly glad to be hanging around for the following stage in my vocation.
"Playing before 62,500 fans at London Stadium will astound. I played here for Burnley last season and I can hardly hold on to encounter it as a West Ham player."
Cornet sparkled for Burnley last season in spite of their transfer, scoring nine objectives and contributing one aid 26 appearances.
West Ham chief David Moyes added: "We are more than happy to invite Maxwel to West Ham United. He is a flexible player with great experience, both in the Premier League and in European football, and will add strength and quality to our crew.
"He had a major effect with his exhibitions for Burnley last season and he has intrigued me with his longing to improve and challenge himself further here at West Ham.
"We anticipate carrying Maxwel into the gathering and want him to enjoy all that life has to offer in his profession with us."
We don't completely accept that Cornet was enrolled before early afternoon [on Friday] so it's impossible he will play for West Ham against Manchester City on Super Sunday.
"His most memorable appearance is probably going to be away at Nottingham Forest one weekend from now."
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