The defending champion Huskies, left in a relatively weak American Athletic Conference after the split of the Big East and the departure of Louisville for the ACC, will host the Buckeyes in December 2015, before traveling to Columbus in December 2016, the schools announced Wednesday.
The Huskies also agreed to visit Arizona's McKale Center during the 2017-18 season and host the Wildcats in 2018-19.
UConn is 2-3 all-time against Ohio State. The teams last met in the Final Four in 1999, with Connecticut winning 64-58 on its way to its first national title.
UConn has won all five of its meetings with Arizona, most recently a 65-53 win in the regional finals during the Huskies' 2011 championship run.