Jets coach Rex Ryan confirmed Tuesday both players won starting jobs.
The team released kicker Nick Novak and punter Chris Bryan Tuesday along with wide receiver Courtney Smith.
"I thought Folk has been kicking outstanding," Ryan said. "When we chart all of our kicks, he's been absolutely outstanding. And quite honestly, Nick Novak had a good camp. I think the competition was good, but clearly I feel that Folk is our guy."
Folk latched on with the Jets after a disappointing 2009 campaign with the Cowboys. He made 30-of-39 field goal attempts last season and was perfect on 37 extra point tries.
The 26-year-old Conley takes the job vacated by Steve Weatherford, who signed with the Giants.