The Dolphins also placed WR Ricardo Louis on injured reserve.
Should Asiata clear waivers, he would revert to the team’s injured reserve list.
Fuller, 25, is a former seventh-round pick of the Texans back in 2017. He agreed to a four-year, $2.5 million contract, but was waived coming out of the preseason last year.
The Texans re-signed Fuller to their practice squad, but he was later signed to the Redskins’ roster. Washington waived Fuller following this year’s draft.
In 2018, Fuller appeared in two games for the Redskins.
Louis, 25, was a fourth-round pick by the Browns out of Auburn in 2016. He signed a four-year rookie deal that was set to expire following the 2019 season.
Louis missed the entire 2018 season because of a neck injury suffered late in 2017. The Dolphins signed him to a one-year contract this past April.
In 2017, Louis appeared in 16 games for the Browns, catching 27 passes for 357 yards (13.2 YPC) and no touchdowns.