Earlier in March, Bournemouth announced that the former Scotland midfielder will leave his position as the technical director at the end of the current season, having taken charge in 2016.
Hughes also had two playing spells at the south coast side between 1998-2002 and 2012-2014.
He replaces Jorg Schmadtke and joins Michael Edwards, who was appointed by Liverpool owners Fenway Sports Group as their Chief Executive Officer of Football last week following 10 highly successful years at the club.
"I am incredibly proud to be offered this opportunity... People rightly talk about the rich history this organisation can boast, but it is the present and future which really excites me," Hughes said in a statement.
"It will be my job, working with Michael and leading the football operations team already in place, plus the wider staff at the AXA Training Centre, to make good decisions."
Hughes will take over responsibilities at Liverpool on June 1st.
Klopp in January announced his decision to step down as Liverpool manager at the end of the current campaign after a trophy-laden eight-and-a-half-years at the club, citing dwindling energy levels.
"As one very successful chapter will come to a close for Liverpool in the summer, the objective of everyone here is for another one to begin - and with Richard I am confident we have the right person in position for us to achieve this aim," Edwards said.
