NFL Media's Ian Rapoport reported the news earlier Wednesday.
The deal is for one year. No salary figures have been disclosed.
"He's excited for the opportunity and his rehab is going strong at this point," said Simms.
Ridley, 26, tore his ACL last October during the Patriots game against the Buffalo Bills. The then-fourth-year player out of LSU had rushed for 340 yards and two touchdowns during the first six games of New England's 2014 campaign.
Johnson was shot last month in Florida, but is in stable condition.
- Will Green