To make room, Cleveland terminated the contract of defensive tackle John Hughes III and waived LB Scooby Wright III.
The Browns, who lost Pro Bowl center Alex Mack to the Atlanta Falcons in the offseason, are preparing to play at the Miami Dolphins in Week 3 without new starting center Cameron Erving. Erving was hospitalized Sunday and diagnosed with a pulmonary contusion. The Browns said Monday, when Erving was released from the hospital, that he would be week-to-week.
Reiter was a seventh-round pick in 2015 and spent most of his rookie season on the practice squad. It would be asking a lot of Reiter to be ready to play five days after joining the Browns, but injuries might dictate just that.
Cleveland will be starting a third quarterback -- rookie third-round pick Cody Kessler -- in three games. Josh McCown (shoulder) started Week 2 but was already ruled out for Sunday's game. Week 1 starter Robert Griffin III (shoulder) could miss 3-4 months.
Whitehurst, who appeared in four games with Indianapolis last season, has played in 24 career contests with San Diego, Seattle, Tennessee and the Colts. He has completed 205 of 372 passes for 2,281 yards and 10 touchdowns during his previous 10 seasons.
Hughes recorded 65 tackles, 5.5 sacks and two fumble recoveries in 53 career contests since being selected by the Browns with a third-round pick in the 2012 draft.
Wright was inactive for Cleveland's first two games after being selected by the club in the seventh round of the 2016 draft.