Gillan was a limited participant at Thursday's practice due to a left groin injury, Dan Salomone of the Giants' official site reports.
The Giants and Gillan agreed on a two-year, $4 million deal Monday, Tom Pelissero of NFL Network reports.
The Browns waived Gillan after removing him from the reserve/COVID-19 list Wednesday, Jake Trotter of ESPN.com reports.
Gillan (undisclosed) won't be available for Sunday's game against the Ravens, Nate Ulrich of the Akron Beacon Journal reports.
Gillan has been placed on the reserve/COVID-19 list Thursday.
Gillan (groin) is active Week 6 against Pittsburgh.
Gillan (groin) is questionable for Sunday's game versus the Steelers, Dan Labbe of Cleveland.com reports.
Gillan (illness) participated in Saturday's practice, Nate Ulrich of the Akron Beacon Journal reports.
Gillan (illness) has not practiced the past two days due to an illness, Scott Petrak of The Chronicle-Telegram reports.
The Browns activated Gillan (illness) from the reserve/COVID-19 list Monday.