The Redskins moved to sign Jackson to a three-year deal and he will now compete against his old club twice a year in the NFC East for the foreseeable future.
Gruden told reporters: "I don't know about any red flags. I know he's a great football player. We met him, I felt great about his character. Time will tell, but I don't foresee any challenges in that regard.
"He's a good player. He's been productive. I think we're excited to have him and anything off the field, we're not concerned about.
"We're counting on DeSean as a player and person moving forward that he's going to be a fit in the locker room and obviously be a great asset off the field."
Jackson recorded 82 receptions for 1,332 yards along with nine touchdowns for the Eagles in the 2013 season.