The 20-year-old playmaker made three appearances for the Reds last season, including a run-out in the Champions League.
Guthrie will complete the relevant paperwork when he returns from his summer holiday.
Wanderers boss Sammy Lee told the club's official website: "Danny is a dynamic midfielder who is very comfortable on the ball.
"He has a tremendous work-ethic and has got a great engine. He is a very good passer who will suit our type of football."
Guthrie joins fellow new arrivals Gavin McCann, Jlloyd Samuel, Gerald Cid, Blerim Dzemaili and Zoltan Harsanyi at the Reebok Stadium.
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