Born in Poland and raised in Berlin, Leo Rapaport and his family arrived in Australia in 1939 as refugees of Hitler's Nazi Germany. His father purchased a small farm in Mount Druitt and it was during this time that he attended Parramatta High School. Perhaps his transition to the school was made somewhat easier, as a teacher at the school Miss Abramovitch had also escaped the tryanny of the Nazis.

After graduating from Sydney University (where he studied Engineering) he joined a firm of electrical and consulting engineers. In 1969, he was awarded the Prince Phillip Award for Industrial Design for an automatic lift system he designed. This led to an invitation from the ABC to appear on The Inventors. In the same year he was elected an Alderman of Sydney City Council (Fitzroy Ward) as a Civic Reform candidate.

He held a number of other positions during his career, including:

In 1975, Leo Port was elected as Lord Mayor of Sydney City Council, a position he held until his sudden death in 1978. Of all his achievements, he has been best remembered for his work with fellow Alderman Andrew Briger, in making the city a place for the people with the installation of trees, a waterall and fountains, an amphitheatre and a square between Town Hall and St Andrew's Cathedral. He was also involved in the restoration of the Queen Victoria Building.

Port was a well-respected member of the Jewish community and a great supporter of a number of synagogues.