Redmond agreed a two-year contract with Burnley, who have the option of further season's extension to his deal.
The 29-year-old was a free agent after leaving Besiktas following a single season in Turkey, where he scored six goals in 28 games.
"I always had aspirations to play again in the Premier League. Burnley's project matches with my ambitions," Redmond said.
"The management team feel like they can enhance my game more and see the value I can bring on and off the field. It feels like a perfect match."
Redmond, who has one England cap, has played 264 times in the Premier League after spending six years at Southampton and three seasons at Norwich.
Burnley manager Vincent Kompany added: "Nathan brings a wealth of experience from playing in the Premier League and more recently from his time in Turkey where he's been outstanding.
"He's got a great work ethic, plenty of skill and a willingness to continue learning. He also brings his personality and character to this football club which will benefit the younger players here."
Redmond is Burnley's fifth close-season signing after their Championship-winning campaign.
Earlier this week, the Clarets brought in Switzerland striker Zeki Amdouni from Basel and England Under-21 goalkeeper James Trafford from Manchester City.
