Allen had only 10 carries for the Giants this year, though only one of those came in the season's final two games.
Allen carried the ball eight times for 28 yards and one touchdown during Sunday's 36-20 win over the Dolphins.
Allen recorded a four-yard rush in Sunday's 31-13 loss to the Packers.
Allen signed with the Giants on Friday, Ralph Vacchiano of SportsNet New York reports.
Allen (undisclosed) was released from the Saints' IR on Friday according to the NFL's official transaction log.
Allen (undisclosed) has been placed on IR, Herbie Teope of The New Orleans Times-Picayune reports.
Allen signed a contract with the Saints on Tuesday, Field Yates of ESPN reports.
Allen worked out for the Saints on Thursday, Josh Katzenstein of The New Orleans Times-Picayune reports.
Allen remains unsigned after the first four weeks of the 2019 league year, Jeff Zrebiec of The Athletic reports.
Allen finished the regular season with 41 carries for 110 yards and three scores while adding 35 catches on 43 targets for 196 yards and two touchdowns.