Edsall traveled to Atlanta earlier this week to talk to Georgia Tech officials about their coaching vacancy.
Edsall informed his team at its annual banquet Sunday that he had withdrawn his name from consideration for the job.
"I'll stay as long as you'll have me," Edsall told the audience.
The news came hours after the Huskies earned a share of the Big East championship in just their sixth season in college football's top division.
When Pittsburgh stunned West Virginia on Saturday, that knocked the Mountaineers (10-2, 5-2 Big East) into a tie with UConn (9-3, 5-2) atop the conference standings.
West Virginia had already secured the Big East's automatic Bowl Championship Series berth because of its 66-21 win over the Huskies on Nov. 24.
"It is something that nobody thought could have happened four years ago or even at the start of this season," Edsall said Sunday. "To have it happen in Year four in the league is a great compliment to the hard work of our student-athletes, assistant coaches and staff."
The title is the latest in a series of milestones reached by the Huskies this season. UConn earned its first national ranking in October, won its first game over a ranked opponent that month, and went undefeated at home (7-0) for the first time in school history.