Tana was spotted playing football at 12, and offered an apprenticeship with Red Star Belgrade. He spent five years at Red Star, developing as a striker. His restaurateur father had been arrested by the new communists authorities established at end of Second World War and led by Marshal Tito, and his restaurants nationalised.
Tana was aged 17 when he toured Belgium in 1952 as part of the junior squad of the Yugoslav football team Red Star Belgrade to play R.S.C. Anderlecht. While in Brussels, Tana abandoned the team and stayed in Belgium.
While in Belgium Tana saw the senior Red Star Belgrade team play Anderlecht, and was spotted in the crowd by the Red Star captain Rajko Mitić. Mitic told Anderlecht of Tana's ability, and arranged a trial for Tana with them. Anderlecht offered Tana a four-year contract, but as a defector he could not play club football in Belgium for two years. Anderlecht loaned Tana to Hannover, and six months later, in the summer of 1955, he was offered a contract to play for Montreal in the Canadian League. Playing in Montreal he won successive Canadian league titles and the Dominion Cup.
After playing poker with a friend, Tana won $5,000, after betting $100, everything they had. With his friend, Luca, Tana decided to go to Hollywood though they had no valid passports. Luca was later taken away by men in a black limousine who Tana assumed were immigration officers. Tana faced the dilemma of whether to return to Canada to resume his football career or remain in the United States, with $10 to his name. He decided to remain in Hollywood, and began working as a dishwasher.
Working as a dishwasher Tana was recognised by a Serb who had seen him play in Canada. With no money, legal papers or a place to stay, the man offered Tana a place to stay and Tana eventually found his way to the Californian league football team Yugoslavian American. The team arranged a job for Tana in a local tuna cannery, and the football contract allowed him to stay in the United States legally.
Tana began drama lessons with Jeff Corey in Malibu, initially to improve his English accent. His drama teacher thought his looks and accent might enable him to play 'bad guy roles' in films. Tana later had a small part in The Enemy Below, starring Curt Jürgens and Robert Mitchum. For the role Tana earned $20,000 for eight weeks work, more than he ever had playing football. Tana also appeared in the films The Untouchables, Rin Tin Tin and Peter Gunn. He rejected an approach from Hannover to return to Europe to play football in 1960, as he was involved in the running of a nightclub, Peppermint West. Tana later became the general manager of the football team L.A. Toros and helped found the first professional soccer league in the United States.
Robert Urich's character in the American television drama Vega$ and Hamish Linklater's character in The Newsroom were both named for Tana. Tana has produced eight films.
In 1973 Tana moved to London, feeling that "... I felt I had more to give to the game and to do that I had to be in a soccer culture. Football was calling me home." Meeting with the English playwright Willis Hall, Hall invited him to join a regular football gathering, which included broadcaster Michael Parkinson and the football personality Jimmy Hill. The manager of Brentford F.C., Frank Bluntstone, attended the gatherings and invited Tana to watch Brentford play. Tana was subsequently asked to join the board of Brentford, a privilege for which Tana bought five shares at 50p each.
Brentford were at the bottom of the Fourth Division at the time of Tana's involvement, and had large debts, and poor attendance. Tana later said that he had had "...big ambitions for Brentford...At that time English football was in trouble...the hooligans and poor facilities made it a very poor form of entertainment for anyone but young men...I wanted to feel comfortable taking my wife and children to a game. In America 30 per cent of the fans in stadia were female. Here it was about one per cent. If America needed English football, England needed American facilities."
Tana became chairman of Brentford and they were promoted and turned a profit. He resigned from the Brentford board in 2002. Tana was also part of the Football Association's International Committee. In 1988 Tana was approached to join the Yugoslav Football Federation by his former team-mate, Miljan Miljanic, then president of the federation. With Yugoslavia Tana attended the 1990 FIFA World Cup, and felt his loyalties divided between both England and Yugoslavia. Tana subsequently prepared a Yugoslav side for the 1992 UEFA European Championship, from which they were banned as result of United Nations sanctions. Tana was elected to the board of Red Star Belgrade in 2000.
Tana has a summerhouse on the island of Hvar in the Adriatic Sea.
Tana founded the restaurant Dan Tana's, on Santa Monica Boulevard in West Hollywood, in 1964. Tana had formerly been the maitre d' at another Hollywood restaurant, La Scala. Since its opening it has been famed for opening late and its steaks, and has been described as "resolutely untrendy" and a favourite of Hollywood and film industry personalities and professionals.