The buyer has been named in an Italian website as Michael Harte, the chief information officer for Australia's Commonwealth Bank, Radio New Zealand reported.
Mura told Unione Sarda his client had lived in several parts of the world and was involved in significant marine and land conservation projects.
Mura said the entrepreneur bought the island, which is home to 'Pink' beach, a national park, with the aim of protecting the ecosystem.
However, the island paradise might not stay in New Zealand hands for long as the Ministry of Environment and the Park Authority has the right to enforce the "right of pre-emption", which allows them to buy the property for the same price paid at auction, within 90 days.
Budelli is an unspoilt island of 1.6 square kilometres where construction is banned and access is only permitted alongside a member of staff from the park's authority.