On January 30, 2016, Miazga joined English Premier League club Chelsea on a four-and-a-half-year deal for a reported £3.5 million (US$5 million). Three days later, he was given the number 20 shirt for the remainder of the 2015–16 campaign.
He was first included in a Chelsea matchday squad on February 16, remaining an unused substitute in their 2–1 loss at Paris Saint-Germain in the first leg of the round of 16 of the UEFA Champions League. With both John Terry and Gary Cahill injured, Miazga made his Chelsea debut starting in a 4–0 Premier League victory away to Aston Villa on April 2, 2016. After an impressive debut, Miazga started his second match against Swansea City, but was substituted at half-time.
On August 31, 2016, Miazga was loaned to Dutch Eredivisie club Vitesse for the 2016–17 season, after a deal with Espanyol fell through due to paperwork. On September 10, Miazga made his debut for Jong Vitesse in a 2–2 draw against SV Spakenburg in the Tweede Divisie The following day, he was on the substitutes' bench for the first-team against Ajax, although he was an unused substitution as Vitesse lost 1–0. He made his Eredivisie debut on September 25, coming off the bench in the 64th minute and provided an assist to Lewis Baker in a 2–1 away defeat to Twente. On December 14, Miazga scored his first and only goal for Vitesse in a KNVB Cup tie against Jodan Boys, which finished 4–0.