The striker was on loan at Stoke City but that agreement was cancelled in order for him to come to Blues.BCFC
The Republic of Ireland international has joined from Aston Villa.
The striker was on loan at Stoke City but that agreement was cancelled in order for him to come to Blues.
Hogan scored both goals in Stoke's 2-2 draw against Derby County and also provided the Potters with their first win of the season with a late strike in October.
But after Stoke changed managers, sacking Nathan Jones, Hogan fell out of favour.
Hogan made his name at Brentford between 2014 - 2017, scoring 21 times in 36 appearances.
That earned him a big money move to Villa. He has 10 goals from 61 appearances for Villa and was loaned out to help Sheffield United clinch promotion at the back end of last season.
Hogan, 27, scored in a 2-0 win against Ipswich Town at Bramall Lane in April which effectively sealed top-flight football for the Blades.
From Salford, Hogan made his way via the non-league ranks before signing as a professional for Rochdale - the club that released him after coming through their youth system - in 2013.
On the back of his 19 goals in 40 games, Rochdale gained automatic promotion to League One in 2013-14.
From there it was on to Brentford, where he impressed during two-and-a-half seasons.
Hogan has been capped eight times by Ireland.
He will wear squad number 40 for Blues.