The former Macclesfield Town player arrives at Celtic after a short spell with Buxton who he had joined from National League side Chesterfield where he had spent two seasons.
Wedgbury began his career at Worcester City before being snapped up by Sheffield United.
He has played for Forest Green Rovers and Wrexham in the National League and has played in the Football League for Mansfield Town and Stevenage, while also enjoying a stint abroad playing for Hungarian champions Ferencváros in 2008/09 when on loan from Sheffield United.
Keep up-to-date with our exclusive email newsletters.
Subscribe