Burlingame was born in Memphis and graduated from Phillips Academy in Andover, Massachusetts in 1960. He studied at Princeton University and worked as a research assistant for David Herbert Donald. Burlingame was a Woodrow Wilson Fellow and Fulbright Scholar. Eventually Professor Donald moved on to Johns Hopkins University and Burlingame followed him there, where he graduated with a Ph.D. in history in 1971.
Burlingame joined the history department at Connecticut College in New London, Connecticut, in 1968 and served there until he retired in 2001. He joined the faculty of the University of Illinois at Springfield in 2009.
Burlingame is a renowned scholar on the life of Abraham Lincoln. He authored The Inner World of Abraham Lincoln (1994) and the two-volume Abraham Lincoln: A Life (2008). The latter won the 2010 Lincoln Prize, was a co-winner of the annual book prize awarded by the Abraham Lincoln Institute, and won the Russell P. Strange Book Award given annually by the Illinois State Historical Society for the best book on Illinois history. Burlingame also edited over a dozen volumes of Lincoln primary source materials.
Burlingame is a board member and officer of both the Abraham Lincoln Association and Abraham Lincoln Institute. In addition to his awards for Abraham Lincoln: A Life, he has received the Abraham Lincoln Association Book Prize (1996), the Lincoln Diploma of Honor from Lincoln Memorial University (1998), Honorable Mention for the Lincoln Prize, Gettsyburg College (2001), and was inducted as a laureate of The Lincoln Academy of Illinois and awarded the Order of Lincoln (the state's highest honor) by the Governor of Illinois in 2009 as a Bicentennial Laureate.
Burlingame has charged several Lincoln scholars with plagiarism. In 2000, Burlingame submitted a review to The Journal of American History alleging plagiarism in John C. Waugh's book, Reelecting Lincoln: The Battle for the 1864 Presidency. In the same review, Burlingame also highlighted errors in citation and transcription in Harold Holzer's book The Lincoln Mailbag: America Writes to the President, 1861-1896. Holzer responded by charging that Burlingame had "riven the Lincoln field, and made it unpleasant to contribute scholarship. He's the Torquemada of academic journalism." In 2002, Burlingame was involved in the Stephen B. Oates controversy, maintaining Oates resorted to plagiarism in his Lincoln biography.