New York was temporarily without a kicker on the roster until he returned in the second half, and then on Monday sources told ESPN's Chris Mortensen that Nugent would be out at least a week with a right quadriceps injury.
"He is very excited to join the Jets and help them keep winning," Feely's agent Glenn Schwartzman said in an e-mail to The Associated Press.
The Jets need to make a move to open up the roster spot for Feely, but hadn't yet officially announced the signing.
Nugent appeared to suffer the injury on a kickoff in the first quarter, limping off the field after a short kick. He attempted a 32-yard field goal later in the quarter but missed wide right, again favoring the injury as he went to the sideline.
Nugent returned for the extra point and the ensuing kickoff after a Jets touchdown in the third quarter to put New York ahead 20-7.
Without another kicker on the roster on Sunday, the Jets were forced to attempt a fourth-and-13 from the Dolphins' 22-yard line in the second quarter. Trying to avoid a sack on the play, Brett Favre heaved a lob near the goal line, which was caught by Chansi Stuckey, who fell into the end zone for a touchdown to put New York ahead 13-7.
The Jets missed the 2-point conversion. Punter Ben Graham handled one kickoff for the Jets.
Feely, cut by Kansas City last month just a day after the Chiefs signed him to a one-year deal, is in his eighth NFL season. He was with Miami last season, going 21-for-23 on field-goal attempts and setting a franchise record with a 91.3 field-goal rate.
Despite his success, the Dolphins cut Feely in August. He had been sidelined with a groin strain that forced him to miss the preseason opener, and his outspoken nature often clashed with the new Bill Parcells-led regime, which has overhauled the roster with younger players.
Feely, 32, will replace Nugent for at least Sunday's game against the New England Patriots.
Information from The Associated Press was used in this report. Chris Mortensen covers the NFL for ESPN.