The Scotland international moves to Turf Moor as a free agent after his deal at former club Blackpool expired.
Gilks made his debut for Blackpool in January 2009 and helped the team achieve promotion to the top flight in 2010 and made over 200 appearances during his time at Bloomfield Road.
He is set to compete with regular first choice Tom Heaton for a spot in Burnley's starting XI next season.
The deal represents manager Sean Dyche's second foray in the transfer market during the present window, after winger Michael Kightly signed a three-year deal on Sunday following a successful loan stint last term.
Michael Duff has also penned a new one-year deal with the club, taking the Clarets' longest-serving player into his 11th season at Turf Moor.
Burnley's season begins with a home match against Chelsea on August 16.