The company says the earliest services will resume is 20 February, three days after the start of central London's congestion charging scheme, and a week later than previously promised.
It will be only a shuttle service between the City and east London.
Services along the full length of the Central Line are expected to resume by mid-March, but only half as often as usual during the rush hours.
Accident
London Underground says it is making "good progress... towards the restoration of services, with extensive tests and modifications being carried out on the entire fleet of trains".
Identical rolling stock on the Waterloo & City line is expected to begin running again on 13 February.
The closure of the two tube lines follows a train accident at Chancery Lane on 25 January.
An inquiry by the Health and Safety Executive is under way into the derailment, in which 32 people were injured.
The investigations team also includes representatives of London Underground as well as Katrina Hyde of the London Transport Users Committee.
Alternative routes
Investigations could take up to four weeks.
The closure of the Central Line and the Waterloo and City Line has resulted in an estimated 600,000 passengers a day having to find alternative routes across London.
London Tube managers insist that there are few accidents on the 140-year-old Underground, saying its record is "second to none".
London Underground managing director Paul Godier said the company would use its "very best endeavours to ensure that a similar accident will not occur in the future".