Huard, 36, is best known for his lengthy backup stints behind Miami's Dan Marino and New England's Tom Brady. Huard started 13 games over the past two seasons with the Kansas City Chiefs, but he never firmly claimed the No. 1 job during five seasons with the team.
"I am thankful that we were lucky enough to have Damon here with us this offseason," 49ers coach Mike Singletary said in a statement released by the team. "He was a professional in every sense. What he did with our quarterbacks was outstanding. He helped them to have a better idea about what it takes to be a pro. ... I really appreciate his professionalism and his personality."
The Associated Press contributed to this report.