In a turnout of half of just under 29,000 members affected by the proposals, 79% voted in favour of the changes while 21% voted against.
Deputy General Secretary Dai Hudd said: "The turnout was one of the highest of any union in such a consultation exercise and
the outcome is decisive in giving clear support to the recommendation of the executive," he said.
"Members have had their say after noting that the proposed terms were the best achievable by negotiation. They understood that the government's offer was conditional on acceptance, and that if the terms were rejected there was a danger of government imposing something much worse.
"However, members also recognised that Prospect had achieved significant improvements from the government's opening position. Indeed, for many, the pension they accrue under the new arrangements could be higher than if they stayed in their current scheme. The final position also protects all those within ten years of retiring, who remain in their existing schemes."
Hudd added Prospect would now be entering discussions alongside the FDA and GMB unions, who had also accepted the proposals, to ensure implementation of the agreement.
The ballot result relates only to the terms of the new scheme operating from 2015, which is closely modelled on the Nuvos scheme already in existence.
"Members do not endorse having to pay higher pension contributions from this year, or the further rises in 2013 and 2014. These increases are an unjustified tax. If you add in the two-year pay freeze and 1% pay cap, members stand to lose around 17% from real-terms pay cuts during 2010-14.
"If the government thinks this result means civil servants are ready to back down, they are wrong. Members will continue to resist the callous attacks on their living standards and campaign for a salary that reflects their specialist skills and compensates for the unfair increases in pension costs imposed on them.
"The focus of our campaign will now turn to pay, where the government's misguided policies are causing real damage to public services."