The inspector, Kevin Moore, had recommended that the hotel be refused planning permission. Mr Moore said the proposed development would "greatly alter the setting of the river, its bridges and streetscape".
"The design of the proposed development is conceptually brilliant but contextually illiterate [because] the proposal has a visually uncompromising impact on Welllington Quay," he said.
Last April, U2's guitarist The Edge told a hearing by An Bord Pleanála that "the future of the hotel might be in doubt" if the owners' redevelopment proposals were rejected.
However, An Bord Pleanála, has disregarded the recommendation of the inspector who held the public hearing into the case.
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There were seven objectors to the plans.
The Clarence owners said in a statement yesterday that they were "delighted" that they got the "green light".
"It's great news for the team that has worked so hard on this project," they said.
As part of the plans, a huge glass atrium will be built over the structure, which is part of the designer's plans to make the Clarence "one of the top ten hotels in the world".
An Bord Pleanála however, have stipulated that the planned 'sky bar' must have public access.
John Redmill, of the Irish Georgian Society said it was a "very black day" for historic buildings.
However, Damien Cassidy of the National Conservation Group said he welcomed the decision.
It is understood Mr Cassidy withdrew his object after U2's lead singer Bono arranged a meeting for him with the architect Norman Foster.
Mr Cassidy says the decision will ensure that the Clarence remains "open for business as a landmark hotel".
U2 members Bono and The Edge, along with property developer Paddy McKillen, can now begin work on the €150 million project to "quadruple" the size of the building and transform it into a "nine-storey, 140-bedroom, five-star hotel".
As part of the approval, the Clarence Hotel will be subject to an archaeologicial assessment of the site.
According to figures released last year, An Bord Plenála rejected the recommendations of its planning inspectors in 603 of 4,611 appeals.
(DS/JM)
