Aslef and the TSSA said good progress had been made in talks and have put off the 24-hours walkouts.
The two unions and the Rail, Maritime and Transport (RMT) union were due to strike on 26 January, and 15 and 17 February.
The RMT will make a decision on Monday.
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The proposed agreement includes a 2% pay rise in year one, RPI inflation or 1% (whichever is greater) in years two and three, and RPI plus 0.25% or 1% (whichever is greater) in year four, plus a Â£500 bonus for staff on lines where the night Tube will run.
LU chief operating officer Steve Griffiths said: "We have had productive talks at Acas."
Finn Brennan, lead negotiator of the train drivers' union Aslef , said: "The determination of our members brought London Underground management back to the table.
"We have dragged them kicking and screaming into the 21st century with an agreement to deliver modern, flexible working patterns for our members and an above-inflation pay rise."
TSSA General Secretary Manuel Cortes warned that the strikes pencilled in for February may still go ahead as the union remains in dispute with LU over "serious issues" surrounding passenger and industry safety.
The RMT said it will hold a mass meeting of representatives on Monday, a day before the first of three strikes is due to start, before making a decision on whether to suspend the strikes.
The Night Tube was due to begin last September but has been delayed after the unions raised concerns over pay and conditions and went on strike over the dispute.
Two unions have suspended planned strikes after London Underground (LU) made an offer on pay over a new night service.