The Niners announced Friday that they have agreed to terms on a two-year deal with Barkley, who went from a career backup to Chicago's starting quarterback during the final six games last season.
Barkley tweeted about his move Thursday night.
Barkley adds to the 49ers' already sizable free-agent class, which includes quarterback Brian Hoyer, who agreed to a two-year deal. Barkley and Hoyer were teammates with the Chicago Bears last season.
The addition of Robinson gives San Francisco three new receivers in free agency, after the team added receiver Pierre Garcon on a five-year deal and receiver Marquise Goodwin on a two-year deal on Thursday.
Among the 49ers' other signings, they added fullback Kyle Juszczyk on a four-year deal, tight end Logan Paulsen on a one-year deal, linebacker Malcolm Smith on a five-year deal and kicker Robbie Gould on a two-year deal.
Barkley, 26, finished last season with 1,611 yards for the Bears -- including three 300-yard passing games -- and eight touchdown passes. He also had 14 interceptions.
He played better than the numbers suggest, however, as the former Southern California quarterback put the Bears in position to win multiple games, only to have Chicago fall short in close situations.
Robinson, 28, spent last season with the Atlanta Falcons under new 49ers coach Kyle Shanahan, who served as Atlanta's offensive coordinator. He had 20 receptions for 323 yards and two touchdowns in 2016, his first season with the Falcons after four seasons with the Washington Redskins.
Coyle originally signed with the Seahawks as an undrafted free agent and spent three seasons in Seattle. He played in 35 games, including five starts, and totaled 24 tackles.
ESPN's Nick Wagoner and Jeff Dickerson contributed to this report.