The agreement allowing for the return of the ceramic pieces, animal and human bones, and metal and stone objects came after Yale and Peru officials announced in November that they had resolved a long-running dispute over the artifacts.
San Antonio Abad University in Cuzco will create a center to house the more than 5,000 objects and fragments.
The center, to be located in an Incan palace and operated under joint direction by both universities, will include a museum exhibit for the public and a research area for collaborative investigations by the two institutions and visiting scholars.
The International Center for the Study of Machu Picchu and Inca Culture will display, conserve and study the Machu Picchu archaeological collections that have been at Yale's Peabody Museum since their excavation by famed scholar Hiram Bingham in 1912.
The Machu Picchu ruins, perched in the clouds at 8,000 feet (2,400 meters) above sea level on an Andean mountaintop, are Peru's main tourist attraction. The complex of stone buildings was built in the 1400s by the Inca empire that ruled Peru before the arrival of the Spaniards in the 16th century.
"This agreement ensures the expanded accessibility of these Machu Picchu collections for research and public appreciation in their natural context and with the guidance of two great universities," said Yale President Richard C. Levin.
Victor Raul Aguilar, rector of the university in Peru, said the agreement "should make us all optimistic that the next century of discovery regarding Machu Picchu will be as rewarding as the last. We hope all who visit Machu Picchu will enrich their experience and understanding of Inca culture with a visit to the center."
Yale faculty and students plan to visit the center for training, research and field work, while Yale will host students and faculty from Peru. The center will loan a small number of artifacts for display at the Yale Peabody Museum of Natural History.
In 2008, the South American nation filed a federal lawsuit demanding the Ivy League university return artifacts taken by Bingham. The claim accused Yale of fraudulently holding the relics for decades.
Yale has said it returned dozens of boxes of artifacts in 1921 and that Peru knew it would retain some artifacts.