The 29-year-old Scot has signed a two-year contract with the Gloucestershire outfit.
Prior to joining Hibs in August 2016, Graham had spells at six other Scottish sides, including Dundee United, St Johnstone and Ross County.
He will be available for Saturday's league visit of Crawley Town, subject to receiving international clearance.
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League Two club Cheltenham Town have signed Hibernian striker Brian Graham on a free transfer.