Johnson, a 6-foot-7 forward, averaged 4.2 points and 3.2 rebounds this past season. Patterson, a 6-2 guard, averaged 2.6 points and 1.7 assists.
Patterson's AAU coach, Chris Hawkins, said the Indianapolis native would possibly look to move to a school closer to home.
Patterson originally signed with Indiana out of high school, but decided to do a post-grad year at Brewster Academy (N.H.) before heading to Syracuse.
The transfers come one day after Syracuse announced its athletic director was being reassigned and coach Jim Boeheim was retiring in three years.
During a news conference Thursday, Boeheim expressed hope that assistant coach -- and presumed coach-in-waiting -- Mike Hopkins would be his replacement. However, Boeheim also said the decision on Syracuse's next head coach was out of his hands.
Among other NCAA punishments, Syracuse was hit with scholarship reductions earlier this month.
The Orange can only use 10 scholarships per year for a four-year period. Prior to the transfers, Syracuse had 11 players scheduled to be under scholarship in the 2016-17 season. The departures of Johnson and Patterson now could enable the Orange to recruit another player in the current junior class.