The 35-year-old has been on loan at Gigg Lane since January, keeping seven clean sheets in his 11 appearances.
The ex-Tranmere, Scunthorpe and Coventry player has not appeared for the Terriers since January 2016.
"I am delighted to have secured the services of Joe Murphy for next season on a permanent basis," said Bury manager Lee Clark.
"He has been an impressive performer since I arrived at the club in February and, coupled with his attitude, desire and winning mentality, it was important we secured his services as soon as possible."
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Huddersfield goalkeeper Joe Murphy has agreed to sign a one-year deal with League One Bury for next season.