Miazga, who made his debut for the Red Bulls shortly after his 18th birthday, has signed a four-and-a-half year contract at Stamford Bridge.
Boss Guus Hiddink confirmed that Miaza has been signed primarily as a "squad player" for the remainder of the season.
Miazga said: 'I am very happy to sign for Chelsea, a world-famous club with a reputation for major success. I am delighted to be in the Premier League, the best league in the world, and can't wait to meet my team-mates and get going.
"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."
Hiddink had been keen to bolster his defensive options after it became increasingly clear a new move for Everton's John Stones will have to wait until the end of the season.
There is also a question mark over the future of Gary Cahill who has become increasingly unsettled with his lack of first-team opportunities.
However Hiddink insisted this week that Cahill would be staying at Stamford Bridge and remained a vital part of his future plans.
