The 30-year-old spent one season with the Spireites before being released this summer.
The forward did not score a single league goal in 18 appearances.
His only goal came from the penalty spot in the FA Cup fourth qualifying round against Curzon Ashton.
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Payne spent the second-half of last season on loan at National League South side Havant and Waterlooville, scoring five goals in 16 appearances.
The experienced striker will be plying his trade in the National League South again with Welling who finished 20th last term, narrowly avoiding relegation.