Terms were not disclosed but a source told ESPN's Adam Schefter that Flowers received a one-year contract.
Flowers, who was released by the Detroit Lions in March, had recently worked out for the Dolphins.
In 2019, the Lions made the two-time Super Bowl champion one of the richest defensive players in football with a $90 million deal over five years with $56 million guaranteed, but Flowers couldn't stay healthy over the past two seasons.
Flowers, 29, was placed on the injured reserve list in the 2020 and 2021 seasons and had just 3.5 total sacks over that two-year span. He had seven sacks in his first season with the Lions, when he played in 15 games.
Flowers is familiar with the defensive scheme employed by defensive coordinator Josh Boyer, having played in similar schemes during his first two seasons with the Lions and also four seasons with the New England Patriots. Boyer is a former Patriots defensive assistant.
Flowers had 21 sacks in his first four seasons with the Patriots. He also had 5.5 sacks in nine postseason games for the Patriots and won two Super Bowl rings with the franchise.
ESPN's Eric Woodyard contributed to this report.