The £14.8bn project's 1,000-tonne boring machine has broken into the eastern end of Liverpool Street Crossrail station.
By 2018 high-speed trains will run from Reading, through central London to Abbey Wood and Shenfield in Essex.
Andrew Wolstenholme, from Crossrail, said the project was on the "final countdown" to link all the tunnels.
The machine, which is named Elizabeth after the Queen, has 2,460ft (750m) to bore until it reaches the end of the line as part of the project's longest tunnelling drive from Limmo Peninsula, near Canning Town, to Farringdon, which is expected to be finished in the spring.
Crossrail's chief executive Mr Wolstenholme said: "We are now on the final countdown to the big east/west breakthrough at Farringdon, which will link all of Crossrail's tunnels for the first time.
"This is a phenomenal feat of civil engineering that London can be justifiably proud of.
"The next challenge is to implement railway systems across the route, keeping the project on time and within budget."
More than 60% of the overall work has been completed for the project.
A sister machine, named Victoria, will reach Farringdon several weeks after Elizabeth.
Crossrail workers have made their latest breakthrough by tunnelling under the City of London.