Cooper was born in Shelbyville. He is the son of former governor Prentice Cooper. He graduated from the University of North Carolina at Chapel Hill, University of Oxford and the Harvard University Law School.

In 1982, he won the Democratic primary for the new 4th District, which had been created when Tennessee gained a district after the 1980 census. His Republican opponent was Cissy Baker, daughter of Senate Majority Leader Howard Baker. This race was closely watched for several reasons beyond the appeal of the offspring of two very prominent Tennessee political figures running against each other. The newly-created Fourth District ran diagonally across the state, from heavily Republican areas near Tri-Cities, Knoxville and Chattanooga to the fringes of the Nashville suburbs. The district stretched across five media markets (the Tri-Cities, Knoxville, Chattanooga, Nashville and Huntsville, Alabama), so the 1982 race had much of the feel of a statewide race. Due to the district's demographics, many felt whoever won it would almost instantly become a statewide figure with a high potential for election to statewide office in the future. Cooper ended up defeating Baker with 66 percent of the vote and was reelected five more times with little substantive opposition, even running unopposed in 1986 and 1988. This was somewhat surprising given that the 4th was, on paper, one of the few districts in the country that was not safe for either party due to its demographics. Indeed, much of the eastern portion of the 4th hadn't been represented by a Democrat since the Civil War. However, he found himself having to explain many of his votes to his somewhat conservative constituents.

In 1994, Cooper ran for the United States Senate for the seat left open when Al Gore was elected Vice President, but was badly defeated by Republican attorney and actor Fred Thompson by the largest margin of defeat in Tennessee history at the time, receiving well under 40f the vote. It was a bad night overall for Democrats in Tennessee, as Republicans captured Tennessee's other Senate seat (in the person of Bill Frist) as well as the governorship. The 4th also fell to the Republicans (in the person of Van Hilleary) as the party gained a majority of the state's congressional delegation for only the second time since Reconstruction. Cooper then moved to Nashville and entered private business, also serving as a professor at Vanderbilt University.

Fifth District Congressman Bob Clement decided to run for Thompson's Senate seat in 2002 after Thompson opted not to run for a second full term, creating the first open-seat race in the 5th District since 1897 (when it was numbered the 6th District). Cooper entered the Democratic primary along with several other prominent local Democrats. The Republicans had long since given up on a district they hadn't won since 1874 (Republicans haven't made a serious bid for the 5th since 1972), meaning that whoever won the Democratic primary was all but assured of being the district's next congressman. Cooper won the primary with 44 percent of the vote, all but assuring him of a return to Congress after an eight-year absence. He was reelected almost as easily in 2004 against a Republican who ran only a token campaign and disavowed his party's national ticket. Given the heavy Democratic tilt of the 5th, it is very unlikely that Cooper will face a serious or well-funded Republican opponent in the foreseeable future.

With his six previous terms of seniority under his belt, Cooper is the only Tennesseean on the Armed Services Committee, and also serves on the Budget Committee.