David Phillips, 67, had denied a single charge of tipping waste in a garage opposite his home in Mount Pleasant in March last year.
But he was convicted at a trial at Swansea Magistrates' Court on Wednesday.
He claimed he believed he was the owner of the garage as the issue had not been challenged in over 20 years. He was fined £200.
He was also ordered to pay £250 in compensation to the legal owner of the garage who had registered it with the Land Registry, unlike Phillips.
He must also pay £2,000 in legal costs and a surcharge of £20 after being found guilty of depositing wood without an environmental permit.
Defence barrister Ben Blakemore called on a number of witnesses, including residents of Oakfield Terrace who admitted to assuming Phillips was the only user of the garage but that they had not known who legally owned it.
In mitigation, Mr Blakemore added: "What we have here is not an offence being committed but a matter of ignorance."
District Judge, Sophie Toms, told Phillips: "I accept your good character and your role in the community and desire to improve it."
The former leader of Swansea council has been found guilty of fly-tipping.