Dens Park manager Neil McCann’s has sprung a surprise by bringing the midfielder to the club.
Roarie Deacon, another midfielder, has also joined Dundee from Sutton United, to become McCann’s first signings since being appointed permanent manager just under a fortnight ago.
Allan, who started his career at Dundee United, is aiming to kick-start his career following a disappointing loan spell at Rotherham.
The 25-year-old made the last of 11 appearances for the Yorkshire club in January before returning to Celtic, where he didn’t feature at all before the end of the season.
Allan signed for Celtic two years ago after appearing on the brink of joining Rangers from Hibs, where he enjoyed a profitable season long spell in 2014-15 under Alan Stubbs, winning the Championship player of the year award.
But he experienced a frustrating first season at Celtic before being sent on loan to Rotherham.