Twenty-four-year-old Cunninghaqm arrives at the Swansway Chester Stadium having last played at Akropolis in the third tier of Swedish football.
Cunningham (pictured), originally from Lincoln, started his career with the Imps in 2011.
Whilst at Sincil Bank, he had loan spells with Worksop Town, Lincoln United, Goole AFC and Eastwood Town.
He has been based in Sweden since being released by Lincoln in 2014, playing for Gallivare FF, Ange IF, Pitea IF and finally Akropolis.
Chester also announced that Jordan Chapell had become the latest senior player to leave the club by mutual consent.
Chapell made nine appearances for the Blues this campaign; as well having a loan spell with Evo-Stik League Premier side Stalybridge Celtic, scoring a hat-trick back in January against Lancaster City.
The 26-year-old made seventy-eight appearances for Chester in all competitions – scoring 8 goals – following his arrival back in 2015.