It will be the 20-year-old's second spell at the club, having joined on loan from Rochdale in 2016.
Bell made nine appearances in 2016-17 for Gateshead, scoring twice.
Earlier on Thursday, Chester - who finished 19th in the National League - announced new deals for midfielder Wade Joyce and utility player Evan Horwood on one-year and six-month contracts respectively.
Chester have signed Gateshead striker Nyal Bell on loan until 7 January.