Branch, 33, was a surprise cut on Aug. 31 when the Patriots trimmed their roster to 53 players. He had spent six of his previous 10 seasons with New England, and was expected to be in the mix near the top of the receiver depth chart.
With tight end Aaron Hernandez likely out for several weeks with an ankle injury, and receiver Greg Salas waived on Tuesday, per a league source, Branch would replenish the Patriots' receiving corps with a familiar face for quarterback Tom Brady.
The Patriots also signed veteran tight end Kellen Winslow to a one-year deal on Tuesday, a source told Schefter.
Last season, Branch started 15 games, catching 51 passes for 702 yards and five touchdowns. He played in 76 percent of the team's offensive snaps in 2011.
Branch's stall in the locker room had stayed intact since his release.
Information from ESPN NFL Insider Adam Schefter and ESPNBoston.com was used in this report.