The Pro Bowl left tackle has agreed to a five-year contract worth more than $45 million, a person familiar with the negotiations said Tuesday.
The person confirmed the agreements to The Associated Press on condition of anonymity because the team hadn't made an announcement.
The deals were part of a busy first day of free agency for new Dolphins general manager Dennis Hickey.
Martin began last season as the Dolphins' starting left tackle. That job will now go to Albert.
''I am now a Miami Dolphin,'' Albert tweeted Tuesday night. ''PhinsUp. Welcoming me with open arms... It's time to work.''
Albert, a first-round draft pick by the Kansas City Chiefs in 2008, started 83 games for them in the past six seasons. He'll move into the position played at the start of last season by Martin, who left the Dolphins in October.
The bullying scandal that then unfolded sabotaged Miami's season. Guards Richie Incognito and John Jerry, both implicated in the case, are among the Dolphins who became free agents Tuesday. Neither is expected back with Miami.
Pro Bowl center Mike Pouncey is the lone offensive lineman involved in the scandal who remains on the roster.
Albert has a home in South Florida, and the Dolphins tried to swing a trade for him a year ago. Instead the Chiefs used the franchise tag on Albert and paid him more than $9.8 million, and he helped them reach the playoffs.
Meanwhile, Martin was a bust at left tackle for the Dolphins, who gave up a franchise-record 58 sacks and finished 8-8.
Albert will be reunited with new Dolphins assistant offensive line coach Jack Bicknell, who coached for the Chiefs in 2012.
Albert tweeted that his move to Miami was ''bittersweet.''
''I want to thank the Chiefs organization and the Chiefs nation and fan base for 6 great years of my career,'' he tweeted. ''Thanks to all the loyal fans that watched me blossom from a boy to a man.... And into a pretty darn football player.... The Chief nation will always be in my heart and have a special meaning to me.... I always appreciate the love and support of the sea of red and yellow.''
Mitchell, a third-round pick by Houston in 2010, became a starter last year. He'll help replace defensive tackles Paul Soliai and Randy Starks, both free agents.
Soliai agreed to terms Tuesday with the Atlanta Falcons.
The Dolphins remain in the hunt for more offensive line help, and they're shopping for a tight end.
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