Coats was graduated from Jackson High School in 1961. He graduated from Wheaton College (Wheaton, Ill.) with bachelor of arts degree in 1965. He served in the United States Army from 1966 to 1968. He earned a law degree in 1971 from Indiana University (Indianapolis). From 1976 to 1980, Coats worked for then U.S. Rep. J. Danforth Quayle III in Quayle's Indiana office. From 1981 to 1988, Coats served in the United States House of Representatives as a representative from Indiana, having been elected to the seat Quayle vacated when he ran for the United States Senate. When Quayle resigned from the Senate after being elected Vice President of the United States in 1988, Coats was appointed to Quayle's former seat. Coats served in the Senate until 1999.

Coats made headlines in August of 1998, when he publicly questioned the timing of President Clinton's attack on terrorist bases in Afganistan and Sudan, suggesting it might be linked to the Lewinsky scandal.

"While there is clearly much more we need to learn about this attack and why it was ordered today, given the president's personal difficulties this week, it is legitimate to question the timing of this action." Coats was also reportedly one of George W. Bush's top choices to be Defense Secretary. Eventually Donald Rumsfeld was chosen instead.

From August 15, 2001 to February 28, 2005, Coats was the U.S. ambassador to Germany.

In 2005, Coats drew attention when he was chosen by President George W. Bush to shepherd Harriet Miers' nomination to the Supreme Court through the Senate. Echoing Sen. Roman Hruska's famous 1970 speech in defense of Harold Carswell, Coats said to CNN regarding the nomination:

"If great intellectual powerhouse is a qualification to be a member of the court and represent the American people and the wishes of the American people and to interpret the Constitution, then I think we have a court so skewed on the intellectual side that we may not be getting representation of America as a whole."