The deal is worth $47 million, with at least $25 million guaranteed, according to the Miami Herald.
"I am pleased to announce that the Miami Dolphins have signed Pro Bowl tackle Branden Albert," said Dolphins general manager Dennis Hickey.
"The addition of a Pro Bowl player of Branden's caliber to our offensive line was definitely a focus of our organization heading into the free agency period. The type of talent, skill and ability that Brandon brings will not only strengthen the offense but will be felt throughout the 53-man roster."
Miami's offensive line was shattered by the bullying scandal surrounding Jonathan Martin and Richie Incognito in 2013.
Martin was traded to the San Francisco 49ers on Tuesday for an undisclosed draft pick.
Albert spent his first six years in the NFL with Kansas City, starting 83 of the 85 games he played in. He was the 15th overall pick in the 2008 NFL Draft and earned his first Pro Bowl nod last year.
The Dolphins allowed a franchise-record 58 sacks last year. Martin left the team before a Week 9 game because of the harassment issue that eventually led to Incognito's suspension soon after.