Miami announced the trade on Tuesday.
Anthony was the No. 31 overall pick in the 2015 NFL Draft. He had 112 total tackles, five passes defended, two forced fumbles, a sack, an interception and a fumble recovery in 16 starts as a rookie. The Pro Football Writers Association All-Rookie team member had 15 tackles in 10 games last season.
Anthony, 25, is listed at 6 foot 3, 245 pounds. He is currently recovering from a high ankle sprain and did not play in the Saints' first two games this season.
The Dolphins are giving the Saints a fifth-round pick for next year's 2018 NFL Draft in the exchange.
Miami desperately needs help at linebacker, especially after last weekend's debacle when starting defender Lawrence Timmons briefly went missing and was inactive for the Dolphins win against the Los Angeles Chargers.
The Dolphins have since suspended Timmons indefinitely.
Mike Hull started in Timmons' place Sunday, leading the Dolphins with seven tackles. The Dolphins held the Chargers to 44 rushing yards.
Miami battles the New York Jets at 1 p.m. Sunday before traveling to London to face the Saints at 9:30 a.m. Sunday, Oct. 1 at Wembley Stadium.