Luton have made their ninth summer signing following the arrival of winger Danny Green.
Notts County have signed Togo international Mawouna Amevor on a two-year deal.
Dudka, who will remain at St Andrew's until January 1, is a holding midfielder who can also play full-back or at the heart of defence
The 29-year-old has been on trial at the Championship club of late, however he is not expected to be available for first-team action for another couple of weeks as he builds up his match fitness.
Boss Lee Clark told the club's official website: "Dariusz spent a long time out and he won't be involved before the international break (in mid-November).
"As we saw last week (during Blues Under-21s' 1-0 defeat to Huddersfield) , it's been a long time since he played a competitive match and, as a result, he will need a mini pre-season."
Dudka is an experienced international for Poland having racked up 65 caps and featured in the 2006 World Cup as well as the 2008 and 2012 European Championships.
He has played for French club Auxerre and most recently Spanish side Levante, whom he parted ways with over the summer.