When fully operational, trains will run from Reading and Heathrow in the west through 13 miles of new tunnels to Shenfield and Abbey Wood in the east.
It will operate as three separate services – as previously planned.
Crossrail says the new line will connect Paddington to Canary Wharf in 17 minutes.
An estimated 200m passengers will use the new undergound line annually, increasing central London rail capacity by 10% – the largest increase since World War Two.
Crossrail Limited described the 10-year project as “hugely complex”.
It said “further time” was required for testing, and that contractors needed to complete work in the central tunnels and to develop “railways systems software”.
Transport for London (TfL) said more time was needed “to ensure a safe and reliable railway for customers from day one of passenger service”.
Lord Adonis, the former Transport Secretary, accused Crossrail of “trying to smuggle out a really serious failure on the biggest infrastructure project affecting the country” when parliament isn’t sitting.
He said: “There’s no excuse for what has happened on this project, and people need to be held to account.”
By Tom Edwards, BBC London transport correspondent
I have lost count of the times that Crossrail executives said to me the project would be delivered “on time and on budget”.
Today that disappeared in a puff of smoke, and there is no doubt this is a blow for Crossrail.
I’m told it wasn’t one specific problem. There were issues with three different signalling systems and also delays to the station fit outs.
They simply ran out of time. This will also hit TfL’s finances which was relying on Crossrail to increase its fare take.
This flagship project – the biggest construction project in Europe – just lost some of its lustre.
The Federation of Small Business (FSB) said it was “extremely disappointed with the news”.
London Policy Chair of the FSB, Sue Terpilowski, said: “Small businesses, particularly in central London, have been preparing for a December roll out of the new infrastructure and to be told on a Friday in August that the date has now changed is simply not good enough.”
A spokesman for Mayor of London Sadiq Khan said the delay is “obviously disappointing.
“It is essential that a safe and reliable railway operates from day one, and this has to be the top priority.”