Linebacker Junior Galette also agreed to re-sign with Washington on a one-year deal, multiple media outlets reported.
Terms of Blackmon's contract were not disclosed, but reports indicated it was a two-year deal.
According to NFL.com, Galette's deal could be worth up to $4.1 million.
Blackmon, 31, played in 15 regular-season games and started 10 for the Redskins last season after signing during Week 2. He finished with a career-high 49 tackles, three forced fumbles and two interceptions.
In 81 career regular-season games, the 10-year NFL veteran has 139 tackles, 20 passes defensed, eight forced fumbles, eight fumble recoveries, three interceptions and 3.0 sacks.
Blackmon has played cornerback, safety and nickel back during his career.
Bruton, a fourth-round draft pick by the Denver Broncos in 2009, has played in 104 career regular-seasons games in seven years in the NFL and seven postseason games, including Super Bowl XLVIII. He has 114 tackles, 16 passes defensed, five forced fumbles, three interceptions, three fumbles recoveries and one sack.
Last year, Bruton logged a career-high 43 tackles, seven passes defensed two interceptions and one sack. Any injury in Week 15 ended his season.
Galette, who turns 28 this month, missed all of last season due to a torn Achilles tendon. It was to be his first year with the Redskins after the New Orleans Saints released him last August.
He started 13 games and played all 16 for New Orleans in 2014, recording 10 sacks, two safeties, three forced fumbles, two passes defensed and 45 tackles. In five seasons with the Saints, he had 31.5 sacks.