He was born in s’Gravenhage, the son of Heinrich Thyssen (1875-1947) and his first wife, Baroness Margit Bornemisza de Kászon (1887-1971). The Thyssen family's fortune was built upon a steel and armaments empire: Heinrich Thyssen had abandoned Germany as a young man and settled in Hungary in 1905. In Budapest, Heinrich married the daughter of the king's chamberlain, who, having no sons of his own, adopted Heinrich and passed on his barony to him. The passing along of the title has raised numerous questions over whether Heinrich Thyssen could actually call himself baron at all.
He married firstly, August 1, 1946, Austrian aristocrat Princess Teresa Amalia Franziska Elisabeth Maria zur Lippe-Weissenfeld (born 1925). Their only child was Georg Heinrich (born 1950). They divorced May 14, 1954, and she married in 1960, as her second husband, Friedrich Maximilian, prince zu Furstenberg.
He married secondly, June 23, 1954, Anglo-Indian fashion model Nina Dyer (1930-1965); they had no children and were divorced on July 4, 1956. She later married and divorced His Highness Prince Sadruddin Aga Khan and committed suicide in 1965.
He married thirdly, September 17, 1956, New Zealand-born British fashion model Fiona Frances Elaine Campbell-Walter (born 1932). She was a daughter of Rear-Admiral Keith McNeil Walter (later Campbell-Walter) and his wife, Frances Henriette Campbell. Their children were Francesca (born 1958 and now married to Archduke Karl of Austria, heir to the defunct Austrian imperial throne) and Lorne (born 1963). They divorced January 20, 1965, and she went on to have a well-publicized relationship with Greek shipping heir Alexander Onassis, the only son of Aristotle Onassis.
He married fourthly, December 13, 1967 Denise Shorto (born 1942), a Brazilian banker's daughter. They had one son, Alexander (born 1974), and divorced in November 29, 1984, after an acrimonious four-year battle.
He married, lastly, August 16, 1985, María del Carmen Rosario Cervera Fernández de la Guerra, known as Carmen "Tita" Cervera, (born 1943), a former Miss Spain 1961. He adopted her son, Borja (born 1980, father unknown). In 1965, she married Lex Barker (1919-1973), an American actor and socialite best known for his portrayal of Tarzan. He had previously been married to Lana Turner and Arlene Dahl. Tita had won an out-of-court settlement in the mid-1970s which effectively left Barker’s youngest son, Christopher, disinherited.
As part of an attempt to dissolve a trust and thereby gain control of her third husband’s assets, she cast doubt on the paternity of Georg Heinrich von Thyssen-Bornemisza, alleging that his father was actually Count Iván Batthyány de Német-Ujvár, the husband of Thyssen's sister Margit: however, a settlement was reached between parties before the baron's death (in Sant Feliu de Guixols, Spain) which brought to a "peaceable" conclusion the wrangling over control of the vast Thyssen art collection, which will remain in Spain.