The source said Bostic will sign a two-year contract with a base value of $5 million and $1.75 million guaranteed. The deal has a maximum value of $6.6 million.
The Redskins had considered other inside linebackers such as Blake Martinez but did not consider them enough of an upgrade to justify the potential cost involved.
Bostic will play in the middle of Washington's base 4-3 defense, which the Redskins are switching to under new coach Ron Rivera and new defensive coordinator Jack Del Rio.
Bostic started every game for the Redskins at inside linebacker last season. He didn't join the team until May 22, after Reuben Foster had torn multiple ligaments in his knee during a voluntary OTA practice.
Bostic, who turns 29 on May 5, eventually established himself because of his leadership and knowledge of the defense. He finished tied for second on the Redskins with 105 tackles, trailing only safety Landon Collins. Bostic also intercepted one pass and recorded one sack.
Finding a long-term home has been difficult for Bostic, a second-round pick in 2013 by the Chicago Bears. He has never spent more than two years with a team. After two seasons with the Bears, he played one year each with New England, Indianapolis and Pittsburgh. The Patriots had traded him to the Detroit Lions in 2016, but a foot injury kept him on injured reserve all season.
Bostic had a productive 2017 season with the Colts, with 97 tackles in 14 games and a career-best six tackles for loss. After that season, he signed a two-year deal with Pittsburgh. He became expendable once the Steelers selected linebacker Devin Bush in the draft.
He has started 62 games in his career, including 44 of the past 46 in which he has played. In his career, he has recorded 419 tackles, 6.5 sacks and 2 interceptions.