The 'International Rugby Experience' will be located on O'Connell Street, and include state-of-the-art interactive exhibitions.
Funding of €10m has also been pledged from JP McManus.
Munster and Ireland rugby legend Paul O'Connell has helped spearhead the project as part of a dedicated committee.
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The Mayor of the City and County of Limerick, James Collins welcomed An Bord Pleanála's decision.
He said: "I'm delighted that planning has been granted for the International Rugby Experience on O'Connell Street and it will be a wonderful addition to the heart of the city centre.
"The new building will no doubt become a landmark as we re-develop our main thoroughfare, making it a must-visit destination for locals and tourists alike.
"Limerick is synonymous with rugby and this new museum will attract rugby fans from around the world wishing to capture and experience the magic and essence of Limerick and rugby.
"The project fits nicely into the plans for Limerick 2030 which will transform Limerick over the next decade."
(CM/MH)
