The team announced the signings on Monday.
Martin, 27, played eight games in 2009 for St. Louis. Before joining the Rams, he spent three seasons in Green Bay. He has 58 career catches for 848 yards and six touchdowns.
Tapp was a restricted free agent, who signed his one-year tender. On his Twitter account, Tapp says it's a "blessing to have a job doing what I love to do."
Tapp played in 16 games with 49 tackles, 2½ sacks and a forced fumble with the Seahawks last season.
Baker spent last year as a backup with New England after seven seasons with the New York Jets. His best year came in 2007 with the Jets when he caught 41 passes for 409 yards and three scores.
Grant started all 48 games during his three seasons in Seattle and has started 144 consecutive games. Grant had 78 tackles and three interceptions last season.
Information from The Associated Press was used in this report.