It means the Irishman, 28, is free to sign a permanent deal with another club despite the transfer window closing at 6pm on Tuesday.
Goodwin moved to the Terriers in the summer of 2008 after turning down a contract extension at Glanford Park, but found first-team opportunities limited when Lee Clark replaced Stan Ternent as manager.
"He is an incredibly hard-working individual who serves as a brilliant example for all of our young professionals and has never let me down when called upon," said Clark.
"I will do everything I can do to help him find a new club but I doubt that he will need any help given his ability."
Goodwin is the second former Iron player to leave Huddersfield by mutual consent this summer, with Andy Butler also departing. The centre-back has yet to sign for another club.