The long-awaited 24-hour weekend service is scheduled to launch on the Central and Victoria lines on August 19.
Transport for London (TfL) says it will be extended to the Jubilee, Northern and Piccadilly lines later this autumn.
It is now understood the Jubilee line will be the first of those to get the new round-the-clock service, from September 2.
'Longer wait due to older trains on Piccadilly line'
There is no date for the Night Tube's introduction on the Northern and Piccadilly lines but train drivers' union Aslef says ageing trains on the latter mean it faces a longer wait.
Finn Brennan, district organiser of Aslef, said: "The Piccadilly line takes longer in terms of driver training, so I would say it's at the back of the queue.
"They're recruiting all new drivers and it has very old stock with manually operated trains, which means drivers need more training.
"Preparations for the Night Tube are going well. Our reps are meeting managers weekly and working to make sure it's implemented smoothly.
"We want it to work because we think it's a good thing for the city and good for our workers."
The Night Tube was originally scheduled to begin last September but its introduction was delayed by disputes between TfL and union leaders.
It will see trains running throughout Friday and Saturday night, as frequently as every eight minutes on certain routes.
'Around 200 drivers undergoing training'
In the longer term, TfL also plans to extend the Night Tube to parts of the Metropolitan, Circle, District and Hammersmith & City lines once modernisation work has been completed.
A TfL spokesperson said: "The start of Night Tube services on the Jubilee, Northern and Piccadilly lines will follow (the initial launch on the Central and Victoria lines) in separate phases later in the autumn as new Tube drivers complete their training and final preparations are made.
"Around 200 part-time drivers are currently taking part in a 14-week training programme to make the Night Tube a reality for London."