The Scotland international, a free agent, joins the top-flight new boys subject to Premier League and FA approval.
Gilks, whose contract at Blackpool expired this summer, spent five years at Bloomfield Road and was an ever-present last season as he reached 200 appearances for the Championship club.
The 32-year-old becomes Burnley’s second signing of the summer, following the arrival of Michael Kightly, and will join up with his new team-mates at the start of pre-season this week.
He said: “I know there’s a strong goalkeeping pool here and Tom (Heaton) was absolutely fantastic last season.
“I’m surprised he didn’t make the divisional team, but he’s been a massive reason why Burnley are in the Premier League, so I know it’s going to be tough.
“But I think in the Premier League you need competition for places and if I can keep the lads here on their toes and between us we help keep the club in this division, then that’s what it’s all about.”
Meanwhile, long-serving veteran defender Michael Duff has signed a new one-year deal at Turf Moor.
Duff remains the only survivor of the squad that reached the Premier League in 2009 and his new deal means the Northern Ireland international will enter his 11th season with the club.
He said: “I spoke to the manager at the end of last season and he said he wanted to keep me. Since then it’s just been a case of sorting out the details.
“I wanted to stay, obviously, because it’s another chance in the Premier League and following the season we had getting there last season.
“It took me until I was 30 to get there the first time around and then I was injured for the first three months.
“That, and getting relegated, made it a disappointment, so to get another opportunity at 36, when you think it may have gone, was something to grab with both hands - and with the team we had last season, plus a few additions, I’m sure we can kick on and surprise a few people.”