The transfer will take place over the course of the upcoming year, and materials will become available for research incrementally, beginning at the end of 2013.
"The Frank Lloyd Wright Foundation takes seriously its responsibility to serve the public good by ensuring the best possible conservation, accessibility, and impact of one of the most important and meaningful archives in the world," said Sean Malone, its CEO.
"Given the individual strengths, resources and abilities of the foundation, MoMA and Columbia, it became clear that this collaborative stewardship is far and away the best way to guarantee the deepest impact, the highest level of conservation and the best public access," Malone said in a statement.
The foundation said it will help guide development of the archives and provide interpretive insights on Wright's work and life.
It will continue to preserve and share Wright's National Historic Landmarks at Taliesin in Spring Green, Wis., and Taliesin West in Scottsdale, Ariz., including historic furnishings, memorabilia and artifacts.
Wright, who died in 1959, designed 1,141 architectural works, including houses, offices, churches, schools, libraries, bridges and museums. Of that total, 532 resulted in completed structures, and 409 of them still stand.
More than one-third of his buildings are listed on the National Register of Historic Places or are in a National Historic District.
He also wrote 20 books, and designed furniture, fabrics, art glass, lamps, dinnerware, silver, linens and graphic arts.