The jury in Newcastle Crown found the men, 39 and 32 years old, guilty of criminal damage. The men, who denied the crime, will receive their sentences on July 15.
The felling of the tree, called Sycamore Gap, took place in 2023 and caused dismay. It had then stood for nearly 300 years on the heath in Hexham in Northumberland, near the Roman Hadrian's Wall, which is listed on UNESCO's World Heritage List.
The tree, an American plane, was known for the lively scenes in the successful film "Robin Hood: Prince of Thieves" from 1991. It has been described as Britain's most famous celebrity tree and a place where people wanted to have their ashes scattered.