Mundell was born in Kingston, Ontario, Canada. He earned his BA in Economics at the University of British Columbia in Vancouver, Canada, and his MA at the University of Washington in Seattle. After studying at the University of British Columbia and at The London School of Economics in 1956, he attended the Massachusetts Institute of Technology (MIT), where he obtained his PhD in Economics in 1956. In 2006 Mundell earned an honorary Doctor of Laws degree from the University of Waterloo in Canada. He was Professor of Economics and Editor of the Journal of Political Economy at the University of Chicago from 1965 to 1972, Chairman of the Department of Economics at the University of Waterloo 1972 to 1974 and since 1974 he has been Professor of Economics at Columbia University. He also held the post of Repap Professor of Economics at McGill University.

In the 1960s, Canada, of which Mundell is a native, floated its exchange: this caused Mundell to begin investigating the results of floating exchange rates, a phenomenon not widely seen since the 1930s "Stockholm School" successfully lobbied Sweden to leave the gold standard.

In 1962, along with Marcus Fleming, he co-authored the Mundell–Fleming model of exchange rates, and noted that it was impossible to have domestic autonomy, fixed exchange rates, and free capital flows: no more than two of those objectives could be met. The model is, in effect, an extension of the IS/LM model applied to currency rates.

Mundell was awarded the Guggenheim Fellowship in 1971 and the Nobel Memorial Prize in Economics in 1999. In 2002 he was made a Companion of the Order of Canada.

This work later led to the creation of the euro and his prediction that leaving the Bretton Woods system would lead to "stagflation" so long as highly progressive income tax rates applied. In 1974, he advocated a drastic tax reduction and a flattening of income tax rates.

In 1992, Mundell received the Docteur Honoris Causa from the University of Paris. Mundell's honorary professorships and fellowships were from Brookings Institution, the University of Chicago, the University of Southern California, McGill University, the University of Pennsylvania, the Bologna Center and Renmin University of China. He became a Fellow of the American Academy of Arts and Sciences in 1998. In June 2005 he was awarded the Global Economics Prize World Economics Institute in Kiel, Germany and in September 2005 he was made a Cavaliere di Gran Croce del Reale Ordine del Merito sotto il Titolo di San Ludovico by Principe Don Carlo Ugo di Borbone Parma.

Mundell won the Nobel Memorial Prize in Economic Science in 1999 and gave as his prize lecture a speech titled "A Reconsideration of the Twentieth Century". According to the Nobel Prize Committee, he got the honor for "his analysis of monetary and fiscal policy under different exchange rate regimes and his analysis of optimum currency areas".

In 2000, he predicted that before 2010, the euro zone would expand to cover 50 countries, while the dollar would spread throughout Latin America, and much of Asia would look towards the yen. Such predictions have proved highly inaccurate.

Mundell has appeared on CBS's Late Show with David Letterman. His first appearance was on October 17, 2002 where he gave The Top 10 List on "Ways My Life has Changed Since Winning the Nobel Prize." In March 2004 he told "You might be a redneck" jokes followed in May 2004 with "Yo Mama" jokes. In September 2004 he appeared again, this time to read excerpts from Paris Hilton's memoir at random moments throughout the show. In November 2005 he told a series of Rodney Dangerfield's jokes. On February 7, 2006 he read Grammy Award nominated song lyrics, the night before CBS aired the 48th Grammy Awards.

Mundell started the Pearl Spring Chess Tournament, a double round robin tournament with six players. The first tournament in 2008 was won by the Bulgarian, Veselin Topalov. The next two: 2009–2010 was won by the Norwegian, Magnus Carlsen.

Mundell has also appeared on China Central Television's popular Lecture Room series. Professor Mundell was also a special guest making the ceremonial first move in Game Five of the 2010 World Chess Championship between Viswanathan Anand and Veselin Topalov.