The ballot closed earlier today (11 July) and the union announced the result on its CWU Live YouTube channel at 4.30pm.
On a 67.1% turnout, 75.84% of members voted yes, and 24.16% voted no.
General secretary Dave Ward said: “The deal has been overwhelmingly endorsed, and we thank you for your support in that.
“But we’re also here to say today that we completely understand how people are feeling at the moment about what’s taking place in the workplace.”
He also warned that if Royal Mail managers “carry on doing exactly the same things they’ve been doing on quality of service, the USO and what’s taking place on revisions, productivity, and all of that it’s going to end in disaster.
“We hope that by you endorsing this agreement, that we can start to have a different discussion now with the company going forward.”
Ward said he believed Royal Mail would announce the identity of its new CEO “in the next week or so” although this was not certain.
The result of the ballot brings to an end a long and bitter dispute that involved 18 days of industrial action last year, which Royal Mail said cost the business some £200m.
Royal Mail posted an adjusted operating loss of £419m for the financial year to 26 March, with sales down 13% at £7.41bn.
Parent group International Distributions Services (IDS) made a £539m impairment charge against the value of Royal Mail, which was included in the reported operating loss.
Following the ballot result, IDS issued a statement and said: "IDS is pleased that members of the CWU have voted in favour of the Royal Mail/CWU Business Recovery, Transformation and Growth Agreement. 75.84% of eligible CWU members participating in the ballot voted in favour of the agreement.
"The agreement provides Royal Mail a platform for the next phase of stabilising the business whilst continuing to drive efficiencies and change. The operational changes in the agreement are designed to be good for customers, increasing our ability to improve services and quality; good for employees, retaining job security and giving people a pay rise; good for the environment, reducing the company's reliance on domestic air, further reducing carbon emissions; and good for shareholders, supporting the long-term sustainability of the business."
IDS said the three-year pay deal would provide certainty for employees "and ensures Royal Mail remains the industry leader on pay, terms and conditions".
