Siemiradzki was born to a Polish noble szlachta family of an officer (since 1871 a General) of the Imperial Russian Army, Hipolit Siemiradzki, and Michalina (née Prószyńska) in the village of Bilhorod (Białogród), or Novobelgorod (now Pechenegi, sources vary) near the city of Kharkov in the Russian Empire, where his father's regiment was stationed. The family had origins in Radom land and derived its name from the village of Siemiradz. One of the branches settled in the late 17th century near Navahrudak (Nowogródek). Henryk's grandfather held the post of podkomorzy in Nowogródek powiat. His parents were close friends with Adam Mickiewicz's family. He studied at Kharkov Gymnasium where he first learned painting under the local school teacher, D.I. Besperchy, former student of Karl Briullov. He entered the Physics-Mathematics School of Kharkov University and studied natural sciences there with great interest, but also continued to paint.
After graduating from the University with the degree of Kandidat he abandoned his scientific career and moved to Saint Petersburg to study painting at the Imperial Academy of Arts in the years 1864–1870. Upon his graduation he was awarded a gold medal. In 1870–1871 he studied under Karl von Piloty in Munich on a grant from the Academy. In 1872 he moved to Rome and with time, built a studio there on Via Gaeta, while spending summers at his estate in Strzałkowo near Częstochowa in Poland.
In 1873 he received the title of Academician of the Imperial Academy of Arts for his painting Christ and a Sinner, based on a verse from Tolstoy. In 1878 he received the French National Order of the Legion of Honour and a Gold Medal of the Paris World's fair for the painting Flower vase. In 1876–1879 Siemiradzki worked on frescoes for the Cathedral of Christ the Saviour (Moscow) among his other large-scale projects. In 1879 he offered one of his best-known works, the enormous Pochodnie Nerona (Nero's torches), painted around 1876, to the newly formed Polish National Museum. The artwork is on display at the Siemiradzki Room of the Sukiennice Museum in the Kraków Old Town, the most popular branch of the museum today. Around 1893 Siemiradzki worked on two large paintings for the State Historical Museum (Moscow) and in 1894 produced his monumental curtain for the Juliusz Słowacki Theatre in Kraków.
He died in Strzałkowo in 1902 and was buried originally in Warsaw, but later his remains were moved to the national Pantheon on Skałka in Kraków.