The 25-year-old is understood to have completed his medical and finalised personal terms on Friday afternoon, after the Hammers activated his £17.5m release clause.
Speaking to West Ham's official website on his arrival at the London Stadium, Cornet said: "It's a new step for me to join this big club and I'm really happy to be here, to be part of the project for the club. I'm just excited to start.
"Everyone knows the level here in the Premier League is very high and I want to play here for that, so I'm really happy to be here for the next stage in my career.
"It will be amazing to play in front of 62,500 fans at London Stadium. I played here for Burnley last season and I can't wait to experience it as a West Ham player."
Moyes added: "We are delighted to welcome Maxwel to West Ham United. He is a versatile player with good experience, both in the Premier League and in European football, and will add strength and quality to our squad.
"He made a big impact with his performances for Burnley last season and he has impressed me with his desire to improve and challenge himself further here at West Ham.
"We look forward to bringing Maxwel into the group and wish him all the best in his career with us."
Cornet began his career with French outfit Metz before leaving in 2015 to join Lyon, where he scored 51 goals and provided 29 assists in 252 games across a six-and-a-half-year spell with the club.
The 29-cap Ivory Coast international then opted to join Burnley last summer for around £13.5m and became a key player with the Clarets despite their relegation from the Premier League.
Cornet, who can operate as a left winger, wing-back or full-back, ended the 2021-22 campaign with nine goals and one assists in 26 top-flight appearances.
The versatile wideman could make his West Ham debut against reigning Premier League champions Manchester City, who visit the London Stadium on Sunday for their opening game of the new season.
Meanwhile, a £33.5m fee plus add-ons has allegedly been agreed to sign Lille midfielder Amadou Onana, although recent reports in the media have suggested that the player favours a move to Frank Lampard's Everton, who are also understood to have had a bid accepted for the 20-year-old. body check tags ::