The 31-year-old was not offered a new contract by the Premier League champions at the end of last season after falling down the pecking order under manager Manuel Pellegrini.
Hull boss Steve Bruce is keen to add to his squad as they prepare for Europa League football next season.
According to Sky Sports News, Lescott has agreed a two-year deal at the KC Stadium, with the option of a further year.
Premier League sides Aston Villa and West Ham United were also said to be interested in signing the former England international.
Lescott joined City from Everton in 2009 for a fee in the region of £22m.