Jaremski was born in Zabrze and represented the club Górnik Zabrze. He competed in 400 m at the 1972 and 1976 Summer Olympics, reaching the quarter-finals both times. In the 4 × 400 m relay he finished fifth with the Polish team at the 1972 Olympic Games. He then won the silver medal at the 1976 Olympic Games with his teammates Ryszard Podlas, Jan Werner and Jerzy Pietrzyk.