The acceptance of the deal by unions will clear a big hurdle for the service which was due to begin last September.
The RMT's 10,000 members will start voting on 11 February.
The Night Tube service will take place on five lines - Jubilee, Victoria, Central, Northern and Piccadilly lines - on Fridays and Saturdays.
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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 £500 bonus for staff on lines where the night Tube will run.
But three other unions are still to decide on whether they accept the offer.
BBC London's transport correspondent Tom Edwards said the RMT executive's move was a "big step forward".
The train drivers' union Aslef and TSSA, which represents station staff, are yet to decide, although Aslef is said to be "looking like they will also accept".
But Unite, which represents engineering staff, has turned down the offer and wants further talks, Tom Edwards said.
The RMT union is still in talks with London Underground over a planned strike this weekend over the issue of job losses.

Oliver Schmidt, a former head of VW's engineering and environmental office in the US, admitted to participating in an attempted cover-up after regulators raised questions the "defeat devices".
He faces up to seven years in prison, and up to $400,000 (£306,000) in fines.
The scandal has cost Volkswagen as much as $25bn.
US prosecutors say Volkswagen installed special software in certain diesel vehicles that allowed them to perform better during emissions tests than they did under normal driving conditions.
The emissions were sometimes 30 times higher than permitted under US rules.
Volkwagen sold almost 600,000 vehicles with the devices in the US between 2006 and 2015, and about 11 million globally. The allegations have also prompted probes in other countries.
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Mr Schmidt was informed that the devices had been installed in 2015, after a nonprofit in the US exposed discrepancies and regulators confronted the company, according to court filings.
Mr Schmidt, who was arrested while travelling in Miami, was one of six people charged related to the scheme in January.  The others live in Germany.
The US also charged a former manager at Audi - which is part of Volkswagen - in July.
A Volkswagen engineer last year pleaded guilty on related charges. His sentencing is expected later this month.
Mr Schmidt, who admitted to conspiring to defraud the US and violating the Clear Air Act, is scheduled to be sentenced in December.
In exchange for Ms Schmidt's guilty plea, US prosecutors dropped a charge of wire fraud. Mr Schmidt also agreed to deportation after his release.
Volkswagen has agreed to pay more than $4bn in fines in the US and to spend up to $25bn to satisfy claims from owners and others.
The emissions scandal in the US contributed to a wider backlash against diesel-powered cars, which were once believed to be more environmentally friendly. Four major cities have moved to ban such vehicles by 2025.
Volkswagen was also recently accused of teaming up with other carmakers in a breach of EU cartel rules.

US media report that Tori Castillo, 39, is facing child abuse charges and the children are now with their father.
Onlookers in the car park instructed the five-year-old on how to open the boot from the inside, reports say.
Passersby had noticed the car shaking and noise coming from inside where it was parked outside a Walmart.
The incident happened on Thursday in Riverdale, Utah. It is not clear how long the children were in the boot.
Local police officer Casey Warren told KTVX: "It's never right to lock a child inside of a vehicle, let alone a trunk of a vehicle.
"Obviously there's a lot of things that could go wrong."
He praised the "good Samaritans" who helped the children get out.
Under Utah state law, leaving a child under the age of nine unattended in a vehicle is punishable by a fine or jail time. The law was enacted in 2011 after repeated cases of children dying unattended in hot cars.
The Rail, Maritime and Transport union will recommend its members accept a pay and conditions deal for the Night Tube service, its executive has decided.
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A former Volkswagen executive has pleaded guilty for his role in the German automaker's scheme to cheat US emissions requirements for diesel cars.
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A woman has been arrested in the US after allegedly locking her children, aged two and five, in the boot of her car while she went shopping.