Fewell is scheduled to meet with Bears officials, including head coach Lovie Smith, on Monday. But a source said Fewell has decided to accept the job.
The Bears have a vacancy after Smith announced that he is relinquishing his defensive play-calling duties.
Fewell, who took over in Buffalo when Dick Jauron was fired in November, was interviewed by the Bills for the head coaching position on Monday.
After his interview with the Bills, Fewell said he came away "optimistic," but still considers himself a long shot for the job.
He also met with the New York Giants this past week about their vacant defensive coordinator's job.
Fewell broke into the NFL in 1998 as a defensive secondary coach in Jacksonville under Coughlin. He also worked two seasons with Smith in both St. Louis and Chicago.
In completing his 12th NFL season, Fewell had no previous head-coaching experience before going 3-4 after Jauron was dismissed. He did become the first of Buffalo's five interim coaches to win more than two games in the season he took over, surpassing the win totals of Hank Bullough (2-10 in 1985) and Marv Levy (2-5, 1986).
Information from The Associated Press contributed to this report.