Ogbah reached agreement on a four-year, $65 million deal that includes $32 million fully guaranteed at signing while Edmonds agreed to a two-year, $12.6 million contract that includes $6.1 million guaranteed, agent Drew Rosenhaus told ESPN's Adam Schefter.
Ogbah was the Dolphins' priority to re-sign among their own free agents after they used the franchise tag on tight end Mike Gesicki last week.
Edmonds gives the Dolphins a possible feature running back for new head coach Mike McDaniel's offensive attack.
He won 14.4% of his pass rushes over the past two seasons, the 22nd-best mark of any NFL defensive lineman. His 18 sacks rank fifth of any defensive lineman since he signed with the Dolphins in 2020, and his 48 disruptive dropbacks (sacks, interceptions, batted passes plus passes defended) are the most in the league.
Ogbah is highly effective at the line of scrimmage, batting down 30 passes since 2020; the next-closest defensive lineman in the league during that span has 21.
Edmonds set career highs in 2021 with 592 rushing yards and 116 rushes, which was in addition to his 43 receptions for 311 receiving yards.
Edmonds, a Fordham University product, shared the backfield workload with James Conner and missed five games -- four on injured reserve with an ankle injury. He missed the season finale with a rib and toe injury, as well.
Edmonds, who turns 26 next month, improved in each of his four seasons, going from 208 rushing yards in 2018 to 303 in 2019 to 448 in 2020 to 592 in 2021.
He set out last offseason to improve his receiving and he reported to training camp as an improved receiver. He was on pace for a career best last season in receiving yards but the injuries kept him from surpassing his personal mark of 402 yards, which he set in 2020.
Ogbah, who turned 28 in November, was drafted out of Oklahoma State by the Browns in the second round of the 2016 NFL draft.
ESPN's Marcel Louis-Jacques and Josh Weinfuss contributed to this report.