According to BBC Sport, Premier League outfit West Ham were close to signing Barton, who was without a club since the end of last season following his release from Championship side Queens Park Rangers.
However, it was Burnley, who got relegated from the Premier League at the end of the 2014-15 campaign just like QPR, have snapped up the 32-year-old midfielder on a one-year deal.
Former West Ham and QPR star Sinclair, who played with Barton at Manchester City, believes that the former Newcastle United midfielder will be a success at Turf Moor.
Burnley have made a disappointing start to the 2015-16 Championship campaign.
The Clarets find themselves 13th in the league table at the moment with five points from four matches, two points behind sixth-placed QPR.