He made his debut in 2008, defeating Mariusz Radziszewski by points decision. In 2009, Głowacki won vacant Baltic Boxing Union International title, defeating Łukasz Rusiewicz by points decision.
On August 18, 2012, he won the vacant WBO Inter-Continental Cruiserweight title, defeating Felipe Romero by sixth-round technical knockout.
On January 31, 2015, Głowacki won WBO European Cruiserweight title by unanimous decision (118-110, 118-110 and 120-108) against Nuri Seferi.
On August 14, 2015, he won the WBO Cruiserweight title, defeating Marco Huck by eleventh-round knockout.