The Clarets had been looking to bolster their goalkeeping department after losing Martin Dubravka at the end of last season.
Amos had been a free agent since leaving Port Vale at the end of last term and had been training with the PFA pre-season squad.
“I’m really pleased to get the move done and I’m very happy to be a part of this club,” he told the club site.
“I think there’s a good blend of younger and older players here and hopefully, I can bring something to the dressing room with my experience and be part of the senior group.”
Amos began his career at Manchester United and headed to Wanderers in 2015, initially on loan before making the move permanent that summer.
He went on to make more than 50 appearances for the club and had loans at Cardiff City, Charlton Athletic and Millwall.
The shot stopper completed a permanent move to Charlton in 2019 and returned to the North West a couple of years later, signing for Wigan Athletic.
Amos spent the last couple of seasons at Port Vale, making 13 appearances in all competitions last term, including six in League One.
Burnley are preparing for life back in the Championship following relegation from the Premier League last season. The Clarets make the short trip to the Toughsheet Stadium on Boxing Day.
The sides haven’t met in the league since the 2015/16 campaign, and Bolton’s last win in the fixture was in February 2013.
