He will remain with the Pesky Bulls until the end of the end of the 2024/25 season, with the option of a further year.
Koelher, 20, joined the club last summer and has been an ever-present in league and cup, featuring in all 15 of their matches since.
A product of the Steven Gerrard Academy, Koehler featured for Burscough last season before catching the eye of the Cables management team whilst on trial over the summer.
He kept a clean sheet and scored on his Cables debut back in August against Eccleshill United in the FA Cup extra preliminary round, before following this up with another goal on his Northern Premier League debut against Mossley.
He also scored against North Ferriby in the FA Trophy last month, taking his tally for the season to three.
Manager Steven Daley said: “I’m very happy that Nathan has committed to the club long term.
"He’s blown us away since minute one in terms of his attitude and application both in training and in games. We’ve got a great group of lads here, and Nathan has fitted straight into that.
"He’s happy here and you can tell that he’s really taken to the club and the fans, who have welcomed him like one of their own.
"We believe that Nathan is only going to get better the more that he plays and listens to what we are trying to do here, so we are delighted wants to be a part of that, long term.”
Pesky Bulls chairman Tony Zeverona said: “Nathan has really impressed everybody at the club since his arrival in the summer, and he has already become a firm favourite amongst our supporters.
"I am pleased that he has committed his future to Prescot Cables. His signing underlines what the club are trying to build both on and off the pitch.”