He earned an Associate of Arts degree from Community College of Baltimore in 1967, a Bachelor of Science degree from the University of Maryland, College Park in 1976, and a Juris Doctor from the Columbus School of Law at the Catholic University of America in 1979.

From 1979 to 1982, Quarles was a law clerk to Judge Joseph C. Howard Sr. of the U.S. District Court for the District of Maryland.

After working in private practice from 1981 to 1982, he joined the U.S. Attorney's Office in Baltimore, where he served as an Assistant United States Attorney until 1986.

He reentered private practice at Venable LLP in 1986 and remained with the firm until he became an Associate Circuit Judge for the Circuit Court for Baltimore City in 1996.

On January 7, 2003, Quarles was named to the federal bench by President George W. Bush, to a seat vacated by William M. Nickerson.