Fr Joseph McAuley, 66, was walking in woodland when he tripped over the stump of a bench which had been left in undergrowth.
He landed face-first on a concrete stump at a park in Cumbernauld, North Lanarkshire, and smashed an eye and nasal socket and severed nerves.
He was rushed to the Southern General Hospital in Glasgow's facial injuries unit where he underwent emergency surgery.
The parish priest at St Lucy's Church in Cumbernauld had three months off work after the 2010 incident.
He launched a personal injuries action against the trust, which manages the park, for failing to warn about the stumps. The case was due to be heard at Airdrie Sheriff Court but the trust agreed to pay Fr McAuley an undisclosed sum.
He said: "I am glad the matter has now been settled and they have accepted responsibility."
Fr McAuley did not want to be accused of cashing in on the UK's compensation culture but said somebody had to take responsibility for safety failures.
He added: "If organisations are going to open parks to the public then they have to be responsible for your safety in them."
Simon Milne, chief executive of the Scottish Wildlife Trust, said: "This was an unfortunate accident and the trust is glad Fr McAuley has made a good recovery."