Karras agreed to a one-year deal worth $4 million, a source told ESPN's Jeremy Fowler. Roberts told ESPN's Josina Anderson that he also agreed to a one-year deal.
The additions of Karras and Roberts came two days after former New England linebacker Kyle Van Noy agreed to sign with the Dolphins and reunite with former Patriots defensive coach Brian Flores.
Karras likely will slide in as the Dolphins' starting center and replace Dan Kilgore, who became a free agent after Miami declined his option. Karras is the second starting offensive lineman to choose the Dolphins in free agency, joining Ereck Flowers.
The Dolphins finished 5-11 in their first season under Flores but played much better down the stretch, winning five of their final nine games and upsetting the Patriots in New England in Week 17.
The Patriots turned to Karras after David Andrews was diagnosed with blood clots in his lungs at the end of the preseason, elevating Karras to the top spot after three seasons with the club in a backup role.
Karras entered the NFL as a 2016 sixth-round pick of the Patriots out of the University of Illinois. He played center in 2019, but he previously started three games at guard in New England.
Karras' great-uncle Alex Karras was a Hall of Fame defensive lineman with the Detroit Lions before going into acting, including a starring role in the 1980s sitcom "Webster."
Elected a Patriots captain for the first time in 2019, Roberts was credited by Bill Belichick and teammates for his selfless work in adding fullback duties to his repertoire after the club had a run of injuries at the position.
Roberts, who turns 26 next month, would practice at linebacker and fullback, although he made it clear in discussions with reporters that he was a hard-hitting defender first. Because of the Patriots' depth at linebacker, Roberts' playing time on defense was limited, usually in run-specific packages. He totaled 29 tackles and one sack in 16 regular-season games.
As a fullback, he opened holes in the running game and contributed a 38-yard touchdown reception in the regular-season finale. Roberts entered the NFL as a 2016 sixth-round draft choice out of the University of Houston.
ESPN's Mike Reiss and Cameron Wolfe contributed to this report.