The restoration of Bluebottle was funded by the Leith-based attraction over an 18-month period.
The Royal Yacht Britannia Trust said the dragon class keelboat was “formerly owned and much-loved” by Philip.
It will join yachts Coweslip and Bloodhound – both of which were also owned by Philip – at the popular Leith site, which has had a “long-standing ambition” to reunite the three historic vessels.
David Heritage, of David Heritage Racing Yachts, was funded by the trust to restore Bluebottle.
He said: “It was a great honour to undertake the challenge of rebuilding such an iconic and famous racing yacht and with the use of modern boat building techniques, bring her back to full racing condition.
“It was also an honour to know that the Duke of Edinburgh was able to see photographs as the rebuild progressed, but equally sad that he was unable to see the finished boat.”
The duke served as a Royal Navy officer and was a keen sailor who was appointed admiral of the Royal Yacht Squadron.
He began sailing while he was at Gordonstoun School in Moray and often took a young Prince of Wales on to the water in Bluebottle, which was a wedding gift to the Queen from the Island Sailing Club in Cowes, Isle of Wight.
In 1956 Bluebottle was loaned to the British sailing team competing at the Melbourne Olympics, winning a bronze medal with Lieutenant Commander Graham Mann at the helm.
The restored yacht is expected to compete for the Edinburgh Cup at the British Dragon Association’s UK championships in late August, crewed by sailors Julia and Graham Bailey.
Royal Yacht Britannia chief executive Bob Downie said: “To finally have all three beautiful royal sailing yachts on public display alongside Britannia completes a historic maritime jigsaw we started 12 years ago, and I am sure our visitors will be as delighted as we are to see all the Duke of Edinburgh’s much-loved sailing yachts united once more.
“We also look forward to Bluebottle once again sailing in the company of other dragon class yachts, both here in the River Forth and at regattas elsewhere in the UK.”