Greene was released by the 49ers in a salary cap move.
"Even though we anticipate an increase in the salary cap, it won't be enough to allow us
to keep Rod and Kevin at their current salaries," team vice president Dwight Clark told the Sacramento Bee.
Greene was cut by the Panthers after the two sides could not agree to a new contract.
The Panthers then signed Renaldo Turnbull, who was cut earlier in the week by the Saints.