Gibbs made the announcement on Twitter, and the news was confirmed to ESPN.com by Gibbs' former AAU coach Gary Charles.
Gibbs chose the Huskies over Ohio State, Pittsburgh, NC State and VCU. The 6-foot-2 guard will be eligible immediately next season after graduating from Seton Hall.
A second-team all-Big East performer, Gibbs averaged 16.3 points and 3.8 assists this past season. He spent the last two seasons at Seton Hall after beginning his career at Texas.
Gibbs is the second graduate transfer to join Kevin Ollie's program this offseason. Former Cornell forward Shonn Miller (16.8 points per game, 8.5 rebounds per game) announced his commitment last month. UConn is also adding four-star recruits Jalen Adams and Steven Enoch to a team that will bring back four starters.