On a digital ballot where 54.0% of eligible members voted, 78.5% approved of the offer.
Another consortium, GMB Scotland, accepted the payment offer earlier in the week.
The pay offer – made to 160,000 NHS staff, including nurses, midwives and paramedics – equates to an increase of 6.5% on average in 2023/24.
It also includes a commitment to updating the “Agenda for Change”, which is nearly 20 years old, to support workforce recruitment, sustainability and retention.
Unison Scotland chair of the health committee Wilma Brown said: “While accepting this offer of payment removes the specter of an industrial strike, there is no room for complacency.
“This deal does nothing to solve the NHS Scotland staff crisis.
Government commitments to revising the working week, achieving fair pay increases on promotion and tackling the workforce crisis must make rapid progress.
“They must also be supported with new money to ensure patients and staff get the NHS benefits they deserve.”
The union’s chief health officer, Matt McLaughlin, said: “This deal was agreed after extensive talks between government, unions and employers.
“There is now a need to get around the table to solve the NHS staffing crisis in Scotland.
“Patients wait too long for routine procedures and staff work under unacceptably stressful conditions.
Unison has agreed to return directly to talks with the government to review nursing, reduce staff vacancies and take a look again at NHS pay structures.
“The NHS must be fit for purpose so that staff can provide a world-class service.”
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