The Royal Navy personnel gathered at Portsmouth Naval Base, Hampshire, to "splice the mainbrace" - a celebration involving drinking a tot of rum.
In a signal to navy personnel across the globe, First Sea Lord Admiral Sir George Zambellas said: "I recently had the pleasure of sending loyal greetings and warmest good wishes, on behalf of the Royal Navy, to Her Majesty The Queen on the birth of HRH Prince George of Cambridge.
"Her Majesty sends all officers, ratings and other ranks of the naval service her good wishes and has graciously given her approval to splice the mainbrace.
"I am delighted that Her Majesty The Queen has recognised the Royal Navy in this way."
Among the sailors joining the Portsmouth celebration was 20-year-old Able Seaman Jamie Hey, who is about to join HMS Dragon in the Mediterranean as a warfare specialist.
He said: "I have been in the navy three years and this is the first time I have spliced the mainbrace. I think it is important to continue these sorts of traditions in the navy."
Splicing the mainbrace has its origins in the days of sail and refers to fixing the main brace of a sail that had broken - usually in a storm or battle. Such a repair was strenuous work and it was customary for sailors carrying out the task to be rewarded with an extra ration of rum.
Nowadays the order to "splice the mainbrace" is issued to mark special occasions such as a change of monarch, birth or wedding.