Ostrom had been an Indiana University faculty member since 1965.
"Indiana University has lost an irreplaceable and magnificent treasure with the passing of Elinor Ostrom," IU President Michael McRobbie said in a statement. "Throughout her lifetime, Lin has brought distinction to the university though her groundbreaking work, which received the ultimate recognition in 2009."
Through her research, Ostrom demonstrated how common resources forests, fisheries, oil fields or grazing lands can be managed successfully by the people who use them, rather than by governments or private companies.
"What we have ignored is what citizens can do and the importance of real involvement of the people involved versus just having somebody in Washington ... make a rule," Ostrom said the day her Nobel Prize was announced.
She said some people had discouraged her from seeking a doctoral degree when she applied for graduate school, but that she loved studying economics.
She is survived by her husband, Vincent Ostrom, a retired political science professor with whom she founded IU's Workshop in Political Theory and Policy Analysis.
The university said Ostrom was diagnosed with pancreatic cancer in late 2011. Nonetheless, following her diagnosis she traveled to India and Mexico, and taught a graduate seminar, the university said.
Ostrom was born and grew up in Los Angeles, and she studied at UCLA. She graduated in three years then worked in the private sector before entering graduate school and receiving master's and doctoral degree in political science from UCLA.
She moved to Indiana when her husband was hired for the political science faculty. She was at first hired by the university, she said, because the political science department needed someone to teach a 7:30 a.m. class.