The 25-year-old Switzerland international will spend the 2022/23 campaign with Chelsea, who have an option of a permanent transfer at the end of the season.
On switching to Stamford Bridge, Zakaria said: "I want to say hi to all the Chelsea fans.
"I'm very happy and proud to be a Blue and I cannot wait to see you soon at Stamford Bridge."
Chelsea chairman Todd Boehly said: "Denis is a talented midfielder with lots of quality and skill. He will add depth and range to our squad this season, and we are looking forward to watching him play in Chelsea blue."