Gregory, 22, made five appearances last season for the Albion after joining from Prescot, with injuries preventing him from featuring more often.
The midfielder now returns to Cables for the 2021/22 season for his second stint, having made 31 appearances in the curtailed 2019/20 season before making the move.
He said: “I really enjoyed my time here previously. It is a great club with a great set of lads in the dressing room as well as an excellent fanbase.
"Once I spoke to the gaffer about his ambitions for the club, it was a no-brainer for me to re-join. The gaffer’s vision for the future and ultimately, his interest in me being a part of that were big factors in me returning. I can’t wait to get going and enjoy my football again.”
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