Tomasz Jaszczuk first appeared in national long jump competitions in 2008. In January he became Polish U18 indoor champion straight away. At the beginning of his athletics career, he also competed in sprint courses up to 200 meters. In July 2009 he took part in the U1 World Championships in Brixen, Italy. He jumped 7.50 m in the final and ended up in fourth place. A few weeks later he was also in the open air Polish U18 champion with a top performance of 7.52 m. In 2010 he could not improve, it was not until 2011 that he managed to set new records. The highlight of this was the U20 European Championships in Tallinn, where he won the silver medal with his first jump over the eight-meter mark. Overall, he jumped 8.11 m. He has been competing with adults since 2012. In June he was able to win his first national title. In the same month he also took part in the European Championships for the first time in Helsinki . He went straight to the final, in which he finished eighth of a total of twelve places with 7.90 m. Since 2012, Jaszczuk has been Polish champion a total of eight more times, five times outdoors and three times indoors.
In 2013 Jaszczuk took part in the U23 European Championships in Tampere, where he finished sixth. In 2014, he improved his personal best to 8.15 m before competing at the European Championships in Zurich. He came in the final on 8.07 m and finished seventh. In the following two seasons he did not come close to his bests. It was not until 2017 that he was able to take part in international championships again at the European Indoor Championships in Belgrade in March . After successfully qualifying, he jumped in the final, personal indoor best performance of 7.98 m, with which he was fourth. Two months later he also jumped his personal best in the open air with a jump of 8.18 m. In August he was finally able to take part in the World Championships in London. He clearly failed in the qualification.
In 2018 Jaszczuk took part in the European Championships in Berlin in August . He jumped the second largest distance of his season in the final and was able to take fifth place. In 2019 he again took part in the European Indoor Championships . He came in the final on 7.80 m and was sixth. In August, he and the Polish team won the European Team Championships in his Polish homeland. Two months later, he finished seventh at the World Military Games in Wuhan.