The 21-year-old, who was released by Tranmere in the summer, has been a key part in Bury's promotion push this season and put in a string of eye-catching performances.
Boss Alan Knill has moved quickly to keep Jones at Gigg Lane and the player himself had no hesitation in extending his stay.
Earlier, Knill spoke of how he rates Jones and fellow Shaker Elliott Bennett among the best wingers in League Two.
The duo shone against Exeter on Saturday, although the Shakers had to settle for a 0-0 draw on the south coast.
Jones and 20-year-old Bennett, on loan from Wolves, will aim to do the same at home to Aldershot this Saturday as Knill's men aim to step up their promotion push.
Knill said: "When they're on form, I think the wingers are as good as anything in the league.
"I must admit, I enjoy watching them play. You just have to allow them to express themselves.
"I don't really give them much, they don't need much coaching, I just tell them to 'go and play' because I know what talent they've got.
"They're bright, they want to do well and they want to get better - and they are getting better, which is the main thing.
"They're both really good young players, and Jonah was a really good find for us."
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