Born in Cleveland, Ohio, Eckart attended private schools in Euclid, Ohio and received his B.A. from Xavier University in Cincinnati in 1971. He went on to earn an LL.B. from Cleveland State University, Cleveland Marshall College of Law in 1974, and was admitted to the Ohio bar in 1974. He commenced practice in Cleveland.

Eckart served in the Ohio House of Representatives from 1975 until 1980. Afterwards he was elected as to the U.S. House of Representatives, serving from January 3, 1981 until January 3, 1993. He was not a candidate for renomination in 1992.

After his term in Congress, Eckart worked in the American Bar Association's Congressional Process Committee, and was also on the board of the American Institute of Certified Public Accountants. He also served as chair of the United States Delegation to the Conference on Security and Cooperation in Europe. From 2000 to 2003 he served as President and CEO of the Greater Cleveland Growth Association. He currently practices law as a partner of Baker & Hostletler LLP, representing "a variety of clients before Congress, the Executive Branch, federal and state agencies and state legislatures."