Venney, 23, came through the ranks at Grimsby Town and had a spell on loan at Boston United before joining Borough in the summer of 2017.
He said: “I’m very happy to be joining Cleethorpes Town, heard a lot of great things about the club and the quality of the players here. Can’t wait to get the season started and be involved in the push for promotion.”
Manager Dave Smith added: “Excited to bring Josh into the club. He's been outstanding in the NCEL over the last couple of seasons and the best player in his position.
“He fits the style of play, comfortable in possession, moves the ball quickly and works hard. He's young, local and will continue to improve. It's a great signing for us and everyone is going to enjoy watching him play.”
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