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Strike action is suspended pending ministerial approval and a ballot of PCS members over the deal.
Gallery bosses have conceded to almost all of the strikers’ demands.
PCS opposed the privatisation of the gallery's visitor services staff but regretfully were unable to prevent it going ahead. However they have reached an agreement with the gallery and contractor Securitas protecting their terms and conditions.
Securitas have also agreed that new staff will be recruited on terms and conditions “broadly comparable” to those of existing staff. They had already agreed that conditions for existing staff would not change. The union has also won guarantees on rosters and staffing levels.
Securitas will continue to pay workers the London Living Wage plus enhancements, which PCS won during the course of their dispute in April.
PCS general secretary Mark Serwotka said: "We are pleased to have reached this agreement and on behalf of the union I would like to pay particular tribute to Candy, who is looking forward to returning to the job she loves, and to all our members at the gallery.
"We still do not believe privatisation was necessary but we will work with the new company and the gallery to ensure a smooth transition and, importantly, to ensure standards are maintained at this world-renowned institution."
Gallery bosses have agreed to a review of the privatisation after 12 months.
The strikers now plan to use the support they received to launch a national campaign in defence of museums and galleries.