On 17 February 1980, as a member of Polish national expedition led by Andrzej Zawada, Wielicki and Leszek Cichy reached the summit of Everest and, in doing so, they became the first to climb an eight-thousander in the winter. He was also the first to make successful winter ascents of Mount Everest, Kangchenjunga, and Lhotse, three out of four highest mountains in the world.

He climbed Broad Peak during a solo expedition and made the first ever ascent of an eight-thousander from a base within 24 hours. He climbed Dhaulagiri and Shishapangma alone establishing new routes. He also made a solo ascent of Gasherbrum II and Nanga Parbat, a feat that was only witnessed by a few Pakistani shepherds. He participated in a number of expeditions on K2. In 1996, he made an ascent of the mountain along the north pillar together with two Italian climbers.

He organized the 2002-2003 Polish winter expedition on K2, which failed to reach the summit. He made another attempt to climb an eight-thousander in the winter by organizing an expedition on Nanga Parbat (2006-2007) but was forced to turn back due to adverse weather conditions. In 2013, he led an expedition to climb Broad Peak in the winter. On 5 March, Adam Bielecki, Artur Małek [pl], Maciej Berbeka and Tomasz Kowalski [pl] reached the summit for the first time in history during winter (Berbeka and Kowalski died while descending from the mountain). In 2018, he led another unsuccessful expedition to reach the summit of K2 in the winter.

In January 2022, he released his autobiography entitled Solo. Moje Samotne Wspinaczki (Solo. My Solitary Climbs) which "delves into the climber’s circumstances, emotions and motivations that led him to undertake each of his solitary ascents".