After months of negotiations, in April the Welsh Government offered a 5% pay rise, as well as two additional one-off payments for this year.
Nearly four out of five workers balloted approved of the deal, according to Unison.
It comes just days after the Royal College of Nursing announced four further strike days in Wales, after rejecting the pay offer.
Other health unions are still balloting members on the offer ahead of a meeting with the Welsh Government later this month.
Unison official Jess Turner said: “Health workers have sent a clear message.
"Of course, NHS staff want and deserve more, but they've opted to accept this offer and the certainty it brings them.
"This acceptance might end Unison's NHS dispute, but it doesn't solve the significant workforce issues facing the health service."
She added: "The most pressing is tackling the growing staffing emergency and health worker burnout.
"NHS staff have told us they need money in their pockets now to deal with the worsening cost-of-living crisis.
"If this deal goes through NHS staff will receive their pay rise much sooner than in previous years.
"This sets an expectation for the way NHS pay is approached in future in Wales."
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