The Premier League club, who took Brazilian forward Alexandre Pato on loan from Sao Paulo-based Corinthians on Friday, said Miazga had signed a four-and-a-half year contract.
New Jersey born Miazga, 20, was a product of the Red Bulls academy, making his debut for the club when he was 18.
"I am very happy to sign for Chelsea, a world-famous club with a reputation for major success," he told Chelsea's website (www.chelseafc.com).
"I am still at the beginning of my career but I believe this is the place to develop and learn from some of the best players in the world."
The 1.93-metre Miazga plays in central defence and was an integral part of a Red Bulls back four with the best regular-season record in north America in 2015.
He earned his first full international cap when he came on as a substitute in a World Cup qualifier against St. Vincent and the Grenadines in November.
"It's a bittersweet day for the New York Red Bulls," the club's Sporting Director Ali Curtis said.
"We are very happy for Matt to get the opportunity but it is tough to see him leave after coming through our academy to the first team -- there is a different feel when one of your homegrown players leaves.
"We tried everything we could to keep Matt but we understand and respect his desire to play in Europe."
(Reporting by Martyn Herman, editing by Ed Osmond)
