The 30-year-old has joined the Seasiders having found first-team opportunities hard to come by at Turf Moor this term, and will ease an injury crisis at Bloomfield Road.
The former Blackburn and Sporting Lisbon man told the Gazette: "I know a couple of the lads and the manager, so it wasn't a hard decision.
"I've signed to the end of the season and am hoping to get as many games as possible and to enjoy it. I'm really looking forward to the challenge."
Mahon, who has two Republic of Ireland caps, will hope to make his debut against Southampton at the weekend.