Police have launched an investigation following the find in an area off the A198, near to the entrance to Gosford House in Longniddry.
It is unclear whether or not the remains are human and efforts to identify them are now under way.
A member of the public called the emergency services when they made the discovery at about 18:30 on Sunday.
A Police Scotland spokesman said: “Inquiries are ongoing to establish the origin and nature of these items.”
Gosford House is the 19th century seat of the Charteris family and opens to the public in the summer.
Built by the 7th Earl of Wemyss between 1790 and 1800, the manor was used by the British Army during World War II.