Grombchevsky was born on 15 January 1855, in the family mansion in Kaunatava in the Kovno Governorate of the Russian Empire (now Lithuania).

His father, Louis Grąbczewski, partook in the Polish uprising of 1863 and was sent to Siberia, while his estate and property were confiscated.

In 1873 Grombchevsky entered the Saint Petersburg Mining Institute but left before completing his studies to join the Life Grenadier Regiment of the Imperial Russian Guard at Kexholm.

In 1886 he led another in the Central Tian Shan Basin and Naryn (upper reaches of the river Syr Darya).

Grombchevsky then entered the astronomical faculty of St. Petersburg University, where he received theoretical and practical skills in surveying, geodesy, and cartography, after which he returned to Turkestan.

He represented the Russian "Red Cross" in Morocco during the war between Spain and France with local insurgents (1908–1909).

Finally, he returned to Poland, where he worked in the State Institute of Meteorology and wrote many books about his travels in Central Asia.