The 18-year-old is currently sidelined with a knee injury he sustained during Liverpool's pre-season campaign, having been included in the first-team squad after scoring 28 goals for the club's Under-18 side last term.
The exact length of his new contract has not been disclosed by the Reds, but it will tie the striker down for the foreseeable future.
"It's a great feeling obviously. I was disappointed to get my injury at the start of the season, but it's a great feeling and it shows that the club has got faith in me. Now I can just focus on my rehab and get back on the pitch," Glatzel told the club's official website.
"I've been at the club for so long and I just want to keep going and see where it takes me. Hopefully I can crack on now and keep going. The contract makes it easier.
"Mentally, it's good to be able to focus on the rehab and know that there's people that have faith in me and they know I'll come back from my injury stronger and I'll be ready when I'm back on the pitch."
Glatzel helped Liverpool to win the FA Youth Cup last season, top-scoring with eight goals en route to the trophy. body check tags ::