"The quarterback oughta be able to do his job, and that's what I'm here for, to protect his blindside so he can produce," Albert said during a Wednesday afternoon press conference announcing his free-agent signing.
"I feel like this is a team where my talents can flourish and help the most, and where I could make my legacy even better as a player."
FOX Sports 1 NFL Insider Mike Garafalo reported the deal was worth $47 million over five years with $26 million guaranteed.
Albert, 29, was considered one of the top free agents available. Kansas City's first-round pick in 2008, he fills a desperate need as the Dolphins likely will have four new offensive line starters to join veteran center Mike Pouncey.
"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," general manager Dennis Hickey said in a statement. "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."
Hickey, Pouncey and quarterback Ryan Tannehill joined other Dolphins executives at dinner Tuesday night celebrate the signing of the Pro Bowl left tackle.
"Probably the happiest person at the dinner table was Ryan Tannehill," Hickey said at the press conference.
Albert and Pouncey represent two talented players to build around after the unit allowed a league-high 58 sacks last season and was partly to blame for a rushing attack that ranked 26th with an average of 90 yards per game.
"It's important that the offensive line gels," Albert said. "You got guys like Mike Pouncey and Branden Albert, guys that have been around and can bring other guys along and make sure you gel and listen to the coaches and get things right... you try to get things right early and often."
The Dolphins talked to Kansas City about acquiring Albert last year, but the trade talks fell through.
"I really didn't think anything of it," Albert said. "Everything could be a rumor. Things might not transpire, which it didn't. I ended up not coming here last year so I can't really worry about it."
Albert also didn't dwell on the Dolphins' infamous bullygate scandal, which involved several offensive linemen. Jonathan Martin, who left team in October claiming he was being bullied and harassed, was traded to San Francisco on Tuesday night.
"I'm not worried about what happened last year or previously what was going on," Albert said. "I'm worried abut the future of the Miami Dolphins. It starts today."
Hickey said Albert was an obvious get for Miami.
"He's always been a targeted guy from the first day I got here," said Hickey, who became GM on Jan. 26. "He's the first guy that Coach (Joe) Philbin and I sat down and watched. As we continued to do our research and watched more film and talked collectively about him, it was clear he was going to be the target addition to our team."