Ogiński was born in Guzów, Żyrardów County (near Warsaw) in the Polish Kingdom (part of the Polish-Lithuanian Commonwealth). His father Andrius was Lithuanian nobleman and governor of Trakai, in Lithuania; his mother, Paula Paulina Szembek (1740–1797), was a daughter of the Polish magnate, Marek Szembek whose ancestors were Austrians and Yadviga Rudnicka who was of polonised Lithuanian descent (family name's root is of Lithuanian origin and the suffix indicates polonisation of her family name).

Taught at home, young Ogiński excelled especially at music and foreign languages. He studied under Józef Kozłowski, and later took violin lessons from Viotti and Baillot.

Ogiński served as an adviser to King Stanisław August Poniatowski and supported him during the Great Sejm of 1788–1792. After 1790, he was dispatched to Hague as a diplomatic representative of Poland in the Netherlands and was Polish agent in Constantinople and Paris. In 1793, he was nominated to the office of the Treasurer in Lithuania. During Kościuszko Uprising in 1794, Ogiński commanded his own unit. After the insurrection was suppressed, he emigrated to France, where he sought Napoleon's support for the Polish cause. At that period he saw a creation of the Duchy of Warsaw by the Emperor as a stepping stone to eventual full independence of Poland, and dedicated his only opera, Zelis et Valcour, to Napoleon. In 1810, Ogiński withdrew from political activity in exile and disappointed with Napoleon returned to Vilna. Andrzej Jerzy Czartoryski introduced him to Tsar Alexander I, who made Ogiński a Russian Senator. Ogiński tried in vain to convince the Tsar to rebuild the Polish State. He moved abroad in 1815 and died in 1833 in Florence.

As a composer he is best known for his Polonaise 'A Farewell to the Homeland' ('Pożegnanie Ojczyzny') written on the occasion of his emigration to Western Europe after the failure of the Kosciuszko Insurrection