The 29-year-old has signed a two-month deal, which will take him up to 1 January, 2014, pending international clearance.
Dudka is predominantly a midfield anchorman, where his tackling and intercepting skills come to the fore, but he can also step in as a full-back or central defender if required.
Blues boss Clark decided to offer him a contract having impressed on trial at Wast Hills during the last couple of weeks, during which time he also played for the Blues U21s
Dudka has 65 Poland caps to his name and represented his nation at the 2006 World Cup and the 2008 and 2012 European Championships.
Dudka was a free agent after leaving Levante in the summer. During his year with the Spanish outfit he made just a solitary appearance due to an injury-hit season.
However, prior to that he was with leading French side Auxerre for four years, where he made 110 appearances and scored six goals. He also appeared for them in the UEFA Champion's League.
Dudka, who will wear first-team squad number 34, isn't likely to be involved in senior action until after the forthcoming international break as he undergoes a 'mini pre-season'.
Blues boss Lee Clark explained: "Dariusz spent a long time out and he won't be involved before the international break. As we saw last week (during Blues U21s' 1-0 defeat to Huddersfield Town U21s) , it's been a long time since he played a competitive match and, as a result, he will need a mini pre-season."
Having began his senior career at Amica Wronki, Dudka spent three years in the Polish top flight with Wisla Krakow before moving to France in 2008.