Williams was scheduled to make $8.485 million (none guaranteed) in 2017 and was to count $10.5 million against the Dolphins' cap.
Albert, a former first-round pick and Pro Bowler with Kansas City, is 32 and is set for a substantial payday in a market saturated with offensive tackles.
They also cut defensive tackle Earl MItchell, not cheap himself at $16 million over four years (signed in 2014) and cornerback Ifo Ekpre-Olomu.
The release of Ekpre-Olomu is not salary-cap related. He mentored Tunsil, who was a three-year starter at left tackle at MS and played mostly guard as an National Football League rookie after he was taken 13th in the draft.
The Dolphins drafted Laremy Tunsil in the first round of the 2016 draft.More news: Rights Group accuses Syria of 8 chemical attacks in Aleppo
It's been widely believed that the Dolphins were grooming Tunsil to be their long term answer at left tackle.
None of the recent releases were complicated decisions for the Dolphins because of age, injury history, or lack of productivity.
The release of 2006 No 1 overall pick Williams was expected after a disappointing season in Miami.
He didn't play a full season in any of his three seasons with the Dolphins because of injuries, including a dislocated wrist last season that he had surgically repaired in November.
Williams, 32, had just 1.5 sacks last season. Last season he was limited to nine games (five starts) because of a calf injury. He started all 35 games he played for the Dolphins, including 12 last season.