Jorge was born in Rome on 22 February 1944, the eldest son of émigré Prince Irakli Bagration-Mukhrani, head of the Mukhraneli branch of the Bagrationi dynasty who had fled Georgia following the Bolshevik Revolution. His Italian mother, Maria Antonietta Pasquini, daughter of Ugo, Count di Costafiorita, died at his birth. In 1946 his widowed father married Princess María de las Mercedes de Baviera y Borbón, a daughter of Prince Ferdinand of Bavaria and a granddaughter of King Alfonso XII of Spain, which drew the Bagrationi family into the dynastic circles of Western Europe. Jorge spent the greater part of his adult life in Marbella, Spain, eventually relocating to Georgia in his final years.
Bagration began competing in motorsport in 1959, initially with motorcycles, and switched to cars in 1963, racing across various series over the following two decades.
He made two attempts to enter Formula One. His first, at the 1968 Spanish Grand Prix entered with a Lola, was refused by the organisers. His second opportunity came at the 1974 Spanish Grand Prix, for which he acquired a Surtees TS16 and was placed on the original entry list. The attempt foundered through an unusual bureaucratic failure: the outgoing president of the Spanish Motor Sport Federation mislaid the entry list when clearing his office. When a new list was compiled, Bagration — who was also dealing with reduced sponsorship — was omitted. Whether his funding difficulties would ultimately have allowed him to start remains uncertain, but his rightful place on the original entry list was never restored, ending his Formula One ambitions definitively.
Turning to rallying, Bagration found his most sustained success. Driving a Lancia Stratos HF, he won the Spanish Rally Championship in both 1979 and 1981, establishing himself as a serious and accomplished competitor at national level. He retired from motorsport in 1982.
The House of Bagrationi is among the oldest Christian royal dynasties in Europe, having reigned over the kingdom of Kartli and Kakheti until 1801, when Tsar Alexander I of Russia annexed the territory in violation of the Treaty of Georgievsk. Many members of the dynasty were subsequently deported to Russia; others fled following the Russian Revolution of 1917.
On the death of his father on 30 October 1977, Bagration became claimant to the headship of the Georgian royal family in exile and adopted the style of Royal Highness. He held the titles Duke of the Lasos, Prince of Kakhetia, Kartalia and Mukhraneli, and served as Grand Master of the Order of the Eagle of Georgia and the Tunic of Our Lord Jesus Christ, and as Protector Egregio of the Divisa of the Old Cavalry and Devotion of San Miguel the Milagroso.
In 1991, following Georgian independence, the Georgian government and parliament formally recognised him as head of the former royal family, despite competing claims from other branches of the Bagrationi dynasty. Jorge made his first visit to his ancestral homeland in 1995 to inter his father's ashes. He subsequently moved from Marbella to Tbilisi, where his sons David and Irakli were living.
Jorge Bagration of Mukhrani died in Tbilisi on 16 January 2008 from complications of hepatitis. On 20 January 2008 he was interred among the kings of Georgia at Svetitskhoveli Cathedral in Mtskheta, one of the holiest sites in the Georgian Orthodox tradition and the traditional burial place of the Georgian monarchy.
His first wife was María de las Mercedes Zornoza y Ponce de León. Their children included Princess María Antonieta, Prince Irakli — who renounced the succession — and Prince David Bagration of Mukhrani, born 24 June 1976, who married Ana Bagration-Gruzinsky, daughter of Prince Nugzar Bagration-Gruzinsky (head of the rival Kakhetian branch), at the Tbilisi Sameba Cathedral on 8 February 2009. Their son Giorgi Bagration Bagrationi was born in 2011. By his second wife, fellow racing driver Nuria Llopis y Oliart, Jorge had a son, Prince Gourami Ugo Bagration, born 14 February 1985.