Robinson, who began his career at Leeds in 1998 and also played for Tottenham and Blackburn, was capped 41 times for his country.
He joined Burnley in January 2016, making three Premier League appearances last season as cover for Tom Heaton.
Robinson, who made 498 club appearances, decided to retire after the recurrence of a back problem.
"My back problem returned towards the end of last season and has prevented me being ready for the start of the new season," he said.
"I have been very lucky to play for four very special football clubs and my country."
Robinson was the England keeper at the 2006 World Cup in Germany, keeping four clean sheets in five games including the goalless quarter-final which Portugal won on penalties.
But he paid the price for costly errors as England failed to reach Euro 2008, most famously failing to connect with a Gary Neville back pass which resulted in an own goal in the 2-0 defeat in Croatia.
Robinson finally retired from international football in August 2011.
Burnley's former England goalkeeper Paul Robinson has announced his retirement at the age of 37.