Lecce province in the farming region of Apulia said that the roughly 100 litres (26 gallons) of extra-virgin olive oil made from the fruits of the giant tree would be sent to the White House every year starting this fall.
"The First Lady has launched the 'Let's Move' campaign for a healthier lifestyle and diet... in perfect harmony with the requirements of a Mediterranean diet," the province said in a statement on Thursday.
The initiative is being supported by local farmers including the "Sant'Anna Cooperative," which manages the 1,500 hectares where the tree is located.
The tree has a diameter at its base of 14 metres (46 feet) and can produce up to 600 kilograms of olives a year.
Michelle Obama has had an organic vegetable garden planted in the White House and regularly invites school children to tend it with her.
Last month she appeared in an episode of "The Biggest Loser" -- a US diet reality show -- to promote her campaign against obesity. (AFP)