Koppell was born on December 15, 1940, in New York City. His parents, refugees from Nazi Germany, moved to the Bronx when Oliver was two years old. Koppell attended Bronx elementary schools, the Bronx High School of Science, Harvard College and Harvard Law School, from which he graduated cum laude. While at Harvard College, he founded Let's Go Travel Guides. He is Jewish. Koppell's first marriage ended in divorce. He is now married to Lorraine Coyle Koppell, an attorney who narrowly lost a race for the New York State Senate in 2000 to Guy Velella. He has three children, all of whom were raised in the Bronx and attended Bronx public schools, and five grandchildren. Koppell is active in the Benjamin Franklin Reform Democratic Club. He has been a resident of Fieldston in the Bronx.
On December 16, 1993, Koppell was elected by the New York State Legislature to fill the unexpired term of New York Attorney General Robert Abrams. As attorney general, Koppell successfully brought a lawsuit to allow drivers under the age of 25 to obtain rental cars in the State of New York. In 1994, Koppell sought a full term as attorney general, but lost to Judge Karen Burstein in the Democratic Primary. He finished second, ahead of Brooklyn District AttorneyCharles "Joe" Hynes and prosecutor Eliot Spitzer. In 1998, he again sought the Democratic nomination for attorney general. He finished third in the primary, behind Spitzer, who won, and State Senator Catherine Abate. Koppell finished ahead of Charles Davis, a former staffer for former Governor Mario Cuomo.
He served as a member of the New York City Council from District 11 in the Borough of The Bronx, covering the neighborhoods of Riverdale, Kingsbridge, Woodlawn, Van Cortlandt Village, Norwood, and Bedford Park. He was elected to the Council in 2001, and defeated Ari Hoffnung by a 3 to 1 margin in 2005. On September 15, 2009, Koppell defeated challenger, Tony Perez Casino winning 65% of the vote. Due to term limits, Koppell left the City Council on December 31, 2013.
2014 State Senate Run
In 2014, Koppell ran a David vs. Goliath challenge against incumbent State Senator Jeffrey D. Klein in the Democratic Party primary, and was defeated on a 60 to 40 margin. Koppell ran on the basis of disbanding the Independent Democratic Conference, led by Klein.