Groves was born in Kansas City, Missouri, grew up in Metairie, Louisiana, and graduated in 1966 from De La Salle High School in New Orleans.

In 1970, Groves graduated (summa cum laude, Phi Beta Kappa) from Dartmouth College with an A.B. degree in sociology. He later earned two M.A. degrees (sociology and statistics, both 1973) and a PhD (sociology, 1975) from the University of Michigan.

For much of his career, starting in 1975, Groves worked as a research professor in survey methodology at the University of Michigan. He was also a researcher in the Joint Program in Survey Methodology, housed at the University of Maryland, College Park. In August 2012, he became the Provost of Georgetown University, succeeding James J. O’Donnell.

In 1982 Groves was elected as a Fellow of the American Statistical Association. He was elected to the National Academy of Sciences in 2011 and is a fellow of the American Academy of Arts and Sciences.

On April 2, 2009, Groves was nominated by President Barack Obama to head the Census Bureau. During his confirmation hearings, Republican senators raised concerns based on Groves’ previous actions that he would apply statistical adjustments to populations believed to be undercounted, thereby inflating their numbers and affecting the apportionment of congressional seats. Groves ruled out the use of statistical adjustments during the hearings and his nomination quickly proceeded to the full Senate in May. However, senators Richard Shelby and David Vitter continued to delay his confirmation due to lingering worries regarding statistical adjustments. They also sought assurance from the Obama administration that the controversial community group ACORN would not be involved in grassroots outreach related to the 2010 Census. On July 13, 2009, after several weeks of opposition by the two senators, Senate majority leader Harry Reid used a procedural motion to force a vote that confirmed Groves, 76-15. He took office July 15, 2009.

On June 13, 2014, President Obama announced his appointment of Groves to the National Science Board of the National Science Foundation.