The 47-year-old replaces Adam Nawalka, whose highly-fancied national squad were eliminated in the group stage of the World Cup in Russia.
Brzeczek was a midfielder who captained Poland, won 42 caps, scored four goals and was part of the team that were runners-up at the 1992 Olympics in Barcelona.
He played for a string of Polish and Austrian clubs and had a stint with Maccabi Haifa in a 20-year career.
After retiring he became a coach and led Wisla Plock to a fifth-placed finish in the Polish league last season.
His first match will be away to Italy on September 7 in the new UEFA Nations League.
Nawalka has said he feels responsible for the World Cup disappointment and will stand down as Poland manager on July 30.