Davidson, who was the Browns' assistant head coach/offensive line coach, will take over for Dan Henning, who was fired last week.
Carolina also announced that Dave Magazu, who has served as tight ends coach since 2003, will take over as offensive line coach for Mike Maser, who was also fired last week in a coaching shake-up after Carolina finished a disappointing 8-8 and failed to make the playoffs.
Davidson's hiring likely means coach John Fox wants the Panthers to focus on the running game. Before joining Cleveland, the 39-year-old Davidson spent eight seasons as tight ends/assistant offensive line coach with New England. Corey Dillon rushed for 1,635 yards in 2004, when the Patriots won the Super Bowl.
Davidson left for Cleveland in 2005 and served as the team's offensive coordinator for the final 10 games this season in relief of Maurice Carthon. But Davidson was replaced himself earlier this month by Rob Chudzinski.
"Jeff has worked under some outstanding coaches, has a background with productive offenses and has been part of three Super Bowl victories with the Patriots," Fox said. "He is a highly regarded young coach who has experienced every phase of the NFL as a player and coach and we look forward to having him on our staff."
The Panthers, hampered by numerous injuries, averaged just over 16 points a game, nearly eight fewer than in 2005, when Carolina lost to Seattle in the NFC Championship Game.
Henning was criticized for being too conservative and not getting star receiver Steve Smith more involved in the offense.
"I am excited about this great opportunity," Davidson said. "It is an outstanding staff and I look forward to the challenge that lies ahead."
Davidson beat out Panthers quarterbacks coach Mike McCoy and Cincinnati Bengals quarterbacks coach Ken Zampese, who both interviewed for the position.
Last week Carolina hired former New York Giants defensive coordinator Tim Lewis as secondary coach, replacing Rod Perry, who was fired along with Henning and Maser.