Huw "Badger" Norfolk, 27, is wanted over a communications mast fire last year and an attack on the Bristol Post's headquarters in 2011.
Police said he had links to anarchist communities and the areas of Bristol, Bath, Cheltenham, Pembrokeshire and London but may not be in the UK.
Crimestoppers has also offered a Â£10,000 reward for information.
The Bathampton mast feeds television and radio broadcasts to 80,000 homes.
Two years earlier, 17 windows at the newspaper had been smashed and paint was thrown at the building.
A group later claimed responsibility, saying it deliberately targeted the paper, but did not reveal its identity.
"Norfolk is wanted in connection with these two serious crimes and we're asking the public to help us to find him," said Det Chief Insp Andy Bevan, from Avon and Somerset Police.
"The arson attack at Bathampton mast on January 3 2013 caused damage worth several hundred thousand pounds and affected TV, radio and mobile phone signals to thousands of homes and businesses including sole and small-scale traders and independent businesses that rely on their telephones to work and trade.
"It robbed many people of their only lifeline in the event of an emergency and put the lives of thousands of innocent adults and children at risk."
He said damage totalling thousands of pounds had been caused to the newspaper officers.
"Both incidents caused huge disruption to the lives of innocent people and we're taking them extremely seriously," he added.
The force said the two incidents were part of a much wider investigation into more than 100 incidents of arson and criminal damage.
Anyone who knows where Mr Norfolk is being asked to contact police.
Police have named a man they want to speak to in connection with a series of attacks linked to anarchists.