The 29-year-old, who was born in Kwara, Nigeria, made 31 appearances for the Celts last year, scoring two goals.
Abadaki started his career at Rochdale, before being part of the Hyde team that won promotion from the Conference North.
He also represented Huddersfield Town, Southport, Stalybridge and Workington on loan before making a permanent switch to Northwich Victoria.
After that, the forward played for Ashton United, Mossley, Nantwich Town, Shaw Lane, Buxton and Ramsbottom United.
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