He was born in Tbilisi, Georgia (then part of Imperial Russia), to Prince George Bagration of Mukhrani (1884–1957) and his wife Helena Sigismundovna, née Nowina Złotnicka.

He married (second) Donna Maria Antonietta née Pasquini dei Conti di Costafiorita (1911-1944) in 1940.

She died in 1953, leaving the daughter Mariam (born 1947) and son Bagrat (1949-2017) behind, and Prince Irakli married (fourth) Doña María del Pilar Pascual y Roig (d. 1994), Marquesa de Carsani, in 1961.

[1] Irakli Bagration-Mukhraneli played a prominent role in Georgian political emigration circles and, as an active royalist, remained in opposition to Soviet rule in Georgia.

[1] In April 1942 the German diplomat Friedrich-Werner von der Schulenberg attempted to unite Caucasus émigré leaders from the Northern Caucasus, Azerbaijan, Armenia, and Georgia - including Irakli Bagration - at the "Adlon meeting" in Berlin; however, the émigrés failed to obtain the endorsement of Reichsleiter Alfred Rosenberg's Ostministerium for recognition of independence in return for collaboration with the Axis powers.