Ostrom received the 2009 Nobel Prize in Economic Sciences for research on the ways that people organize themselves to manage resources. She shared the prize with University of California economist Oliver Williamson.
"Indiana University has lost an irreplaceable and magnificent treasure with the passing of Elinor Ostrom," university President Michael McRobbie said in a statement. "Throughout her lifetime, Lin has brought distinction to the university through her groundbreaking work, which received the ultimate recognition in 2009 when she was awarded the Nobel Prize in Economic Sciences."
Ostrom had been an Indiana University faculty member since 1965, the university said. She is survived by her husband, Vincent Ostrom.
Born Elinor Awan on Aug. 7, 1933, in Los Angeles, Ostrom often reflected on being a child of the Great Depression and recalled her family harvesting food from their garden and knitting scarves for soldiers during World War Two.
Ostrom described herself as being a "poor kid in a rich kid's school" at Beverly Hills High School where she swam competitively and joined the debate team.
She worked her way through the University of California, Los Angeles, graduating in three years and entering the workforce before applying to graduate programs.
"Despite resistance to admitting women to doctoral programs" at that time, Ostrom earned masters and doctoral degrees from UCLA, Indiana University officials said.
Ostrom joined the Indiana University faculty in 1965. Her research ranged from the effectiveness of urban police departments to management of groundwater basins, irrigation systems, pasture lands, forests and fisheries, the university said.
McRobbie said Ostrom's love for her students and enduring support of colleagues will leave a legacy beyond the work she and her husband pursued and the university.
"Their generosity to Indiana University was extraordinary as well, with gifts, including Lin's Nobel Prize funds, totaling many millions of dollars," McRobbie said.
Ostrom continued to travel and worked with colleagues on grants and publications, advising and teaching a graduate seminar after was diagnosed with pancreatic cancer in late 2011, the university said.