Professor Bourgain shares the prize with the Australian-American scientist Terrence Tao from the University of California.
Bourgain gained his doctorate from the Free University of Brussels in 1977, before leaving for the U.S. to take up a teaching post at the University of Illinois.
Professor Bourgain is currently one of eight permanent staff at the prestigious School of Mathematics at Princeton University.
The prize will be awarded at a ceremony in April. Professor Bourgain will receive his prize from King Carl Gustaf of Sweden.