Trevathan's deal is worth $24.5 million with $12 million guaranteed, a source told ESPN NFL Insider Adam Schefter.
Entering his fifth NFL season, Trevathan provides a much-needed upgrade to anchor the middle of the Bears' defense. He played three years in Denver under Bears coach John Fox and has a built-in comfort level with Chicago's 3-4 defensive scheme.
General manager Ryan Pace said at the NFL scouting combine that the club has some interest in re-signing McClellin, who is also an unrestricted free agent after the team declined his fifth-year option.
Trevathan had a bounce-back season in 2015 after he spent much of the 2014 season out of the lineup with three separate injuries to his left leg. After the third injury, Trevathan went on injured reserve.
He led the team in tackles in two of the past three seasons, topping 100 tackles in those two years.
But he started all but one game in the regular season in 2015 and all three of the team's postseason games.
Trevathan is a three-down linebacker who has experience in the 3-4 scheme the Broncos played this past season as well as the 4-3 scheme Fox and then-defensive coordinator Jack Del Rio used in his first three seasons with the team.
As Trevathan has put it: "I feel like I can play anywhere anybody needs me to play."
Trevathan, who turns 26 on March 24, was the Broncos' sixth-round pick in 2012.
Cornerback Tracy Porter, who signed a one-year contract with the Bears last summer, will stay in Chicago after coming to a three-year agreement with the team. Porter's deal is worth $16.5 million, according to ESPN and media reports.
Limited to three games in an injury-plagued one-year stint in Washington in 2014, Porter, 29, recovered to become arguably Chicago's most effective cornerback last season. He led the team with 22 pass breakups.
Massie, 26, started 14 games for the Cardinals last season after being suspended for the first two for violating the NFL's personal conduct policy, stemming from a DUI arrest in January 2015.
With 2015 first-round pick D.J. Humphries waiting in the wings for the Cardinals, Massie was credited with giving up 39 quarterback hurries, seven sacks and six hits last season.
ESPN Bears reporter Jeff Dickerson, Broncos reporter Jeff Legwold, Cardinals reporter Josh Weinfuss and Josina Anderson contributed to this report.