The revised offer includes a four-year pay deal and plans for a 36-hour four day week.
Each of the unions warned that if future negotiations fail then there will be more strikes.
Night Tube was to have started on 12 September last year, with 24-hour trains on Fridays and Saturdays along the entire Jubilee and Victoria lines, but LU was unable to reach agreement on pay and working practices with the unions.
Steve Griffiths, LU’s chief operating officer, said it had put forward a “very fair offer.”