In return, the Dolphins will receive linebacker Vince Biegel, reports ESPN's Adam Schefter.
Alonso had apparently requested to be dealt after spending the last three seasons in Miami.
The 29-year-old was thought to be on the trade block or a candidate to be cut for most of the offseason. He racked up 125 tackles, three forced fumbles, and three interceptions last year but was set to see his role diminish in 2019 with Jerome Baker and Raekwon McMillan playing larger roles.
