"He's a three-down linebacker, and he can play both the MIKE position and the WIL linebacker position," Eagles coach Andy Reid said of Witherspoon, who will play the middle. "He's very good at both of them. He's a good cover linebacker. He has the flexibility to cover tight ends and running backs and that type of thing, which is a plus."
Witherspoon has recorded more than 100 tackles three times in his career and has missed only two games due to injury.
Gibson, a sixth-round pick, was inactive for all six games with Philadelphia.
Witherspoon, 6-foot-1½, 239 pounds, was moved from the middle to his more natural weakside position this season by St. Louis to make room for James Laurinaitis, selected with the 35th pick in last April's draft.
"I'm definitely comfortable doing it," Witherspoon said. "It's never bothered me one way or another, when I was lighter or heavier, one side of the ball or the other. I'm a guy who just wants to be out on the field and have an opportunity to make plays."
Witherspoon played this season under new Rams coach Steve Spagnuolo, a disciple of late Eagles defensive coordinator Jim Johnson, so he is already familiar with the Philadelphia system.
"I've gotten pretty comfortable with it," Witherspoon said. "I think I've done a pretty good job of what he asked of me and what was asked of me in the defense and how the other guys around me need to perform and try to maintain my role.
"Overall, there is a lot of similarity, and that will kind of be the good thing about it."
The Eagles have struggled at middle linebacker since projected starter Stewart Bradley tore a knee ligament in a preseason scrimmage in August.
Second-year player Joe Mays was handed the job, but failed to impress. Omar Gaither, liked by the Eagles as a coverage linebacker, was next. He was replaced by recently re-signed Jeremiah Trotter, who had been out of football for over a year.
Trotter was exposed in coverage during last week's 13-9 upset loss at Oakland, and doesn't appear to be the answer. Gaither injured a foot during the loss to the Raiders and could be out of practice this week.
Witherspoon is now joining a team with serious playoff hopes, leaving the 0-6 Rams behind.
"It means a lot to go to a team that has the opportunity to be a contender," he said. "That's what you have to look at. You have to sit there and say, 'OK, take the positives out of everything.'
"I know I'm leaving kind of a comfort zone here, being that I've been here for almost the last four years, but I'm moving into another situation."