Foster tore his ACL in practice Monday. He has not yet had surgery, and doctors fear there could be more damage but won't know until they operate, a source said.
He was officially placed on injured reserve on Wednesday.
Bostic started 14 games for Pittsburgh last season, but the Steelers drafted Devin Bush in the first round. They cut Bostic a day later. Bostic is now with his fifth franchise in as many years -- and sixth overall -- after spending his first three seasons with Chicago, where he was a second-round pick in 2013.
He has made 28 starts the past two years combined, including 14 in 2017 with Indianapolis. He missed 2016 with a foot injury while playing for Detroit. Chicago traded Bostic to New England in 2015 where he made one start and appeared in 11 games.
Foster was going to start inside in the Redskins' base 3-4 defense, providing Washington with a young, fast and athletic linebacker. Without him, they have veteran Mason Foster, second-year Shaun Dion Hamilton and rookie fifth-round pick Cole Holcomb. They also have Josh Harvey-Clemons as a nickel linebacker.