The project was commissioned by Historic Scotland in 2001 as part of a wider effort to restore the king's palace to its 1540s style.
A team of 18 weavers from across the globe came together to reinterpret and create the "Hunt of the Unicorn" tapestries.
Visitors can now see all seven tapestries together for the first time.
In the 1540s, the palace was home to James V's wife, Mary of Guise, and their young daughter, Mary Queen of Scots.
It was known from royal inventories that when James V built the palace he owned more than 100 tapestries, but there is no record of what happened to them. The inventories, however, described a set of tapestries depicting "the historie of the unicorne".
The "painstaking" project to recreate the tapestries involved extensive research and took the team to New York, where the Metropolitan Museum of Art hosts a set of 15th Century tapestries on the same theme.
Peter Buchanan, Historic Scotland's project manager who oversaw the process, said it had been a "privilege to watch" the weavers recreate the tapestries "in all their Renaissance glory".
He said: "Whilst we may never know what happened to the original tapestries, the fact that we now have these fantastic recreations, with the assistance of the Met in New York and through the generosity of our donors, will provide visitors to the castle now, and for generations to come, with a real insight into how the palace may have been at the time of James V.
"The completion of this last tapestry, The Mystic Hunt of the Unicorn, is made all the more impressive by the fact that only two fragments of the original remain in New York.
"Through extensive research, the team were able to build up a picture of how the panel might have looked originally and it's thrilling to see the end result hanging in the palace with the rest of the series, marking the final step in a 14-year journey."
A 14-year project to recreate the lost tapestries of James V has been completed at Stirling Castle.