The application, which involves the demolition of the 41,600-seat stadium and other buildings currently on the site, will be examined by the London Borough of Hammersmith and Fulham.
The council have set a deadline for comments on the application of Friday, 8 January 2016.
The club say that the planning process will last beyond the end of the season.
In a statement on their official club website, Chelsea said that the new stadium would see "facilities improved for every area" and offer an "outstanding view" from every seat in an arena "designed to create an exciting atmosphere".
The new stadium involves both excavation works and the construction of new external concourse areas, including the formation of decking platforms over part of the District Line and part of the Southern mainline railway.
Chelsea have played at Stamford Bridge since 1905, and the ground was last redeveloped in the 1990s.
However, its current capacity of about 42,000 is significantly smaller than the stadia of Premier League rivals Manchester United, Arsenal and Manchester City, whose grounds hold 76,000, 60,000 and 55,000 respectively.
Blues owner Roman Abramovich had initially considered seeking a permanent new home, with the club describing the option of expanding Stamford Bridge as "not feasible or viable" in 2012.
But the club decided to redevelop its current ground because of a lack of suitable sites available in London - having had a bid to build an "iconic" new stadium in Battersea Power Station rejected.
Chelsea have submitted a planning application to build a new 60,000-seat stadium at Stamford Bridge.