San Francisco received the 154th overall selection in the 2020 draft in the deal and used it on West Virginia offensive lineman Colton McKivitz.
Breida, who offers intriguing speed and playmaking ability, was deemed the odd man out in a loaded 49ers backfield. Kyle Shanahan's offense also rostered Raheem Mostert, Tevin Coleman, Jeff Wilson, and Jerick McKinnon at the position.
The 25-year-old will likely share Miami's backfield with Jordan Howard in 2020. The Dolphins rushing attack struggled mightily a season ago with Kalen Ballage and Patrick Laird leading the charge for most of the year.