The official Emirates News Agency reported that Mr Hedges, 31, a Durham University researcher who was arrested at Dubai Airport on May 5, was granted a presidential pardon with immediate effect after his family appealed for clemency.
The agency reported: "The customary National Day Presidential pardon includes Mr Hedges as part of a tranche of clemency orders issued on the occasion of the UAE's 47th National Day anniversary.
"Mr Hedges will be permitted to leave the UAE once formalities are completed."
The agency quoted UAE Minister of State for Foreign Affairs Dr Anwar Gargash saying: "His Highness the President's gracious clemency in the customary National Day pardons allows us to return our focus to the underlying fundamental strength of the UAE/UK bi-lateral relationship and its importance to the international community.
"It was always a UAE hope that this matter would be resolved through the common channels of our longstanding partnership. This was a straightforward matter that became unnecessarily complex despite the UAE's best efforts."
"The case against Mr Hedges was predicated on evidence secured from Mr Hedges' electronic devices; surveillance and intelligence gathering by UAE intelligence and security agencies; and evidence provided by Mr Hedges himself - including a corroborated account of asset recruitment and training and the confidential information being targeted.
"His recruitment and progress within a foreign intelligence service was authenticated to the court by UAE intelligence agencies.
"The gracious Presidential customary National Day pardon allows us to close this chapter and to concentrate on the many positive aspects of the relationship."
Foreign Secretary Jeremy Hunt said on Twitter: "Fantastic news about Matthew Hedges.
"Although we didn't agree with charges we are grateful to UAE government for resolving issue speedily. But also a bittersweet moment as we remember Nazanin & other innocent people detained in Iran. Justice won't be truly done until they too are safely home."