ESPN's Adam Schefter, they got it by trading Jerome Harrison and a seventh round pick for the former Dolphin.
Brown was used sparingly as LeSean McCoy's backup this season by the Eagles. Since he was pretty much a non factor this season with only 13 carries for 28 yards, getting rid of him wasn't too difficult.
For the Lions, getting a back like Brown can be a good thing given the health of starting running back Jahvid Best. Best has a history of concussions and he is dealing with one right now. There is no telling how long he will be out, so having depth with a proven back like Brown gives some stability to a Lions team on the rise.