Rembski was born and raised in Sochaczew, Poland, during Czarist days. The son of a prominent interior decorator, Rembski began drawing animals as a child. He later earned an engineering degree from Warsaw Technological Institute and studied painting at the Ecole des Beaux Arts in Warsaw. At age twenty-three Rembski enrolled at the Royal Academy of Fine Arts in Berlin. While trying to avoid military service in Poland, he was captured by the German army and threatened with execution. Rembski quickly sketched the face of a guard, who invited him to his own house to hide.
After painting German nobility in the early 1920s, Rembski moved to New York, where he set up a studio in Brooklyn and became a U.S. citizen in 1929. A one-man show at Carnegie Hall in 1934 brought him wide acclaim; he painted portraits, murals, and landscapes. In 1938, he discovered Baltimore – allegedly the only city where it was not snowing while Rembski was on his way to Oklahoma to paint Osage Indian Chief Lookout. He settled in Baltimore in 1940, where he continued as a portrait painter, taught a charcoal sketch class, and wrote about art and religion. An exhibition of his portraits was held at the Baltimore Museum of Art in 1947.
During his career, Rembski painted some 1,500 portraits, including those of five Maryland first ladies, Hubert H. Humphrey, Babe Ruth, Brigham Young, and Johns Hopkins. His portraits are in museums and private collections throughout Europe, North America, and Australia. His posthumous portrait of Woodrow Wilson hangs in the Woodrow Wilson Museum in Washington, while his portrait of Franklin D. Roosevelt, commissioned by Eleanor Roosevelt, hangs in his presidential library in Hyde Park, New York. He summered in Deer Island, Maine, where he painted the local fishing scene.
On his 100th birthday, Rembski was the subject of a centennial exhibition of his work at New York’s Salmagundi Club.