James I imported black mulberry trees to England in the early 17th century in an attempt to start a silk industry. He had trees planted on the site of the current palace - but because they were black rather than white mulberries, they were no good for silkworms.
He also had a mulberry planted in 1608 at Charlton House in south-east London, which is looked after by Greenwich Council. The 'Charlton House' mulberry was given to Sir Adam Newton (tutor to James I's son) by James I.
Fraunfelter planted a tree propagated by well-known fruit tree grower Will Sibley from the 'Charlton House' tree at Buckingham Palace. The tree will add to the palace's 30-strong National Council for the Conservation of Parks & Gardens national collection, which it has held for six years.
Palace head gardener Mark Lane said there is a mirror collection at Windsor Castle. He added that five new mulberry trees from UK and US nurseries would be added this year.
The mulberry was the WCF's tree of 2008 as it was its 400th anniversary. Its tree for 2009 is the Bramley apple, which is 200 years old this year.
Fraunfelter said: "It's a treat to put one of James I's mulberries back here."
Lane said the tree was planted to integrate with the garden's landscape rather than as a specimen.
The palace, which is the largest private garden of its type in London, opens for the first time for guided tours this spring.
Around 3,500 people bought tickets and the tour sold out on the same day tickets went on sale. There is now a waiting list of two years for tours.
The 'Charlton House' mulberry is likely to feature in a presentation written by Lane to be given to the visitors to the palace gardens.
Lane will also lead some special curator's tours of the garden.
Footage of the planting will be on the palace's Royal YouTube Channel site at www.royal.gov.uk.
A palace representative said: "The significance of this donation is that it will bring back an old tree into the garden - one that dates from the same time as those that were planted by James I in the early 1600s. Thus one of James I's original trees is returning to the palace gardens and completes a neat little historical circle."