Moore said remaining with the Dolphins appealed to him partly because he expects substantial improvement by a team that has endured four consecutive losing seasons.
"This team is definitely going places," he said. "There are big things to come, and I didn't want to miss out."
General manager Jeff Ireland hopes to re-sign at least a couple of other players before they become free agents. Possibilities include tackle Jake Long, running back Reggie Bush, cornerback Sean Smith, safety Chris Clemons, tight end Anthony Fasano and reserve tackle Nate Garner.
"I am excited that we have been able to reach an agreement with both Brian and Matt to keep them as members of the Miami Dolphins," Ireland said in a statement.
"Brian is an ascending player that has steadily improved over his first four years with the organization. He has represented himself positively both on the field and throughout the South Florida community. Matt has been a valuable contributor to the Dolphins ever since he arrived two seasons ago."
This week's deals leave the Dolphins with enough salary cap room to sign at least one major free agent. On Monday, they designated defensive tackle Randy Starks as their franchise player.