McMahon, the younger brother of former Kop hero Steve, joins Rafael Benitez's backroom staff as reserve-team manager, replacing Gary Ablett.
During three years with the Shrews, McMahon was assistant to both Gary Peters and Paul Simpson.
"It's not often a club like Liverpool comes calling so it's a fantastic opportunity for me," he told BBC Radio Shropshire.
"I've been able to work with youth players right up to first-teamers and I think I've proved myself.
"I'm sorry to leave Shrewsbury as it's a progressive club with good people going in the right direction, but moving to Liverpool is something I can't wait to get my teeth into."