Robertson is the son of Julian Hart Robertson Sr., a textile company executive, and the former Blanche Spencer. He graduated from Episcopal High School in 1951 and the University of North Carolina at Chapel Hill in 1955. While at Chapel Hill, he was admitted to Zeta Psi fraternity. He then served as an officer in the U.S. Navy until 1957.

After leaving the Navy, Robertson moved to New York City and worked for a time as a stockbroker for Kidder, Peabody & Co. At Kidder, he eventually headed the firm's asset management division (Webster Securities) before departing to move with his family to New Zealand for a year to write a novel. On his return, in 1980 Robertson launched Tiger Management with initial Investments from friends and family.

In 1993, his compensation and share of Tiger's gain exceeded $300 million. His 2003 estimated net worth was over $400 million, and in December 2017 it was estimated by Forbes at $4.1 billion. Robertson said in 2008 that he shorted subprime securities and made money through credit default swaps. The following year, according to Forbes, Robertson's return on his $200 million personal trading account was 150 percent.

On April 1, 1996, BusinessWeek carried a cover story written by reporter Gary Weiss, called "Fall of the Wizard", that was critical of Robertson's performance and behavior as founder and manager of Tiger Management. Robertson subsequently sued Weiss and BusinessWeek for $1 billion for defamation. The suit was settled with no money changing hands and BusinessWeek standing by the substance of its reporting.

The Tiger funds reached a peak of $22 billion in assets in 1998. Robertson's Tiger Fund accurately predicted the Tech Bubble, purposely underweighting the sector due to the overpricing of Technology securities in comparison to their earnings and earning potential. So, though Tiger underperformed the S&P 500 in the short term, the fund accurately predicted the underlying flaw in the market. "The proportion invested into Technology stocks by Tiger Management, for Example, a well-known value-manager, is low. In 1999 Tiger eliminated virtually all Investments in this segment. This is consistent with the widely reported refusal of Julian Robertson, manager of the Tiger Fund, to buy into the internet bubble."

After closing his fund in 2000, Robertson kept his hand in the hedge fund Business by supporting and financing upcoming hedge fund managers (38 in total as of September 2009), in return for a stake in their fund management companies. Apart from those, many of the analysts and managers Robertson employed and mentored at Tiger Management, including Chris Shumway, Lee Ainslie and Ole Andreas Halvorsen went out on their own and are now running some of the best-known hedge fund firms, called "Tiger Cubs". These include funds such as Viking Global Investors, Tiger Legatus, Blue Ridge Capital, JAT Capital Management, Tiger Global, Maverick Capital, Coatue Management, Nehal Chopra's Tiger Ratan Capital Fund NA among others.

In 2008, he was inducted into Institutional Investors Alpha's Hedge Fund Manager Hall of Fame along with David Swensen, Louis Bacon, Steven Cohen, Kenneth Griffin, Paul Tudor Jones, George Soros, Michael Steinhardt, Jack Nash, James Simons, Alfred Jones, Leon Levy, Seth Klarman, and Bruce Kovner.

In May 2010 the New York Stem Cell Foundation, a private research institution, announced that it had received a $27 million gift from Robertson and his wife Josie to fund its research. Josephine Tucker Robertson, wife of Julian Robertson, died 8 June 2010 after a long fight against breast cancer.

In January 2012 Robertson donated $1.25 million to Restore Our Future, a Super PAC supporting Mitt Romney's presidential campaign. In 2015, Robertson gave $1 million to a Super PAC supporting Jeb Bush's presidential candidacy. In April 2016, Robertson gave $25M to Success Academy Charter Schools in New York.