The running back made 220 rushing yards and 371 receiving yards during his first season with the AFC West side.
The 31-year-old told the Chargers' official website: "I didn't know where I'd be, but I knew I wanted to come back here. I was excited when I heard from them and I got this opportunity to come back and be here because I established a good relationship with a lot of guys and enjoyed myself.
"It's another opportunity to do what I love to do. At this point you never know if this is going to be the last one, so you want to take advantage. If there is a message or motto I'm going by these days it's embracing the moment.
"I'm embracing the practices and embracing the time I get to be around the guys because once it's over, it's over. I don't think there is anything else you can do that is quite the same. So you've just got to embrace every moment, the good and the bad."
Brown previously had spells with the Philadelphia Eagles and the Miami Dolphins.