Whimper, who started 15 games last season, would have become an unrestricted free agent next week, while Robinson would have been a restricted free agent.
A fourth-round draft pick by the New York Giants in 2006, Whimper joined the Jaguars in November 2010. He has played in 21 games for Jacksonville since.
He likely will return to a backup role this fall, as right tackle Eben Britton returns from back surgery.
Information from ESPN.com's John Clayton and The Associated Press was used in this report.