The former Watford man joined the Bees on a similar deal last summer, making 27 appearances as Paul Fairclough's men staved off relegation from League Two.
Norville missed the final stages of the campaign with an ankle injury, but Fairclough was sufficiently convinced of the 22-year-old's ability to keep the him at Underhill.
"I am delighted to have finally sorted out the contract, and I am looking forward to the new season," Norville said.
"My injured ankle is on the mend and, although I will miss the start of pre-season, I hope to be fit by the time we kick off properly."
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