Having secured his release from Barrow, the striker has signed a two year deal.
The prolific 31-year-old forward was the Blues top scorer in the 2015/16 campaign, with 26 goals in all competitions.
Ross spent last season at Barrow – scoring five goals in 32 appearances.
Hannah’s return makes him the fourth striker to be signed up by Manager Jon McCarthy for next season; following James Akintunde, Harry White and Nyal Bell.
Welcome back to Chester FC, Ross!