Hoke would replace Sean McDermott, who was fired by the Eagles in mid-January.
The Eagles allowed 377 points this season, the most since 1974. Philadelphia won the NFC East with a 10-6 record before losing to the Green Bay Packers 21-16 in a first-round playoff game.
Under Hoke, the Bears ranked ninth overall on defense, second against the rush and tied for third with 35 takeaways this season. Opposing offenses managed just 256 points (16 per game), fourth-fewest in the NFL, and the 14 passing touchdowns allowed by Chicago was the league's second-lowest total.
Chicago won the NFC North with a 11-5 mark, but lost to the Packers 21-14 in the NFC Championship Game.
Hoke spent seven seasons with the Houston Texans before joining the Bears in 2009. His younger brother, Brady, was named head football coach at the University of Michigan earlier this month.
Information from The Associated Press contributed to this report.