Ezra was born in Aleppo, Syria to a Syrian Jewish family. The roots of the Nahmad family are in Aleppo, where his Father, Sephardic Jewish banker Hillel Nahmad lived until just after World War II . Following the Syrian anti-Jewish violence in 1949, his Father moved to Beirut, Lebanon, where Ezra and his brothers sold English novels to US sailors stationed in Lebanon. In the early 1960s, With the rise of Palestinian threat against the Lebanese Republic, Ezra's Father took him and his brothers, Joseph (Giuseppe), David, to Milan, Italy. As teenagers, the three began to deal in art - and skipped school to trade on the Italian stock market.
His son Helly Nahmad is a London-based art dealer. In 2007, his daughter Michaela Nahmad was "thought to be embarking on a career as an art dealer".
As of 2013, Ezra and his brother David are considered influential "mega-dealers" of modern and impressionist art by the most well-known names, from Monet and Matisse to Renoir and Rothko. They own an inventory of between 4,000 and 4,500 works, stored in the duty-free Geneva Freeport warehouse next to the airport in Geneva, Switzerland. The brothers buy and sell most of their works at auction.