A key member of the Magpies' Championship title-winning team of 2009-10, the defender made 138 appearances in black and white, scoring twice.
He won the Premier League title with Leicester City in 2016 and joined non-league Macclesfield Town last season.
Simpson confirmed his retirement on his social media accounts on Friday, posting that his career - which included spells with Manchester United, Queens Park Rangers, Huddersfield and Bristol City - 'was a dream come true.'