Kenny Dalglish looking forward to working with Reds' new man
Clarke's last job was at West Ham as Gianfranco Zola's assistant, but his status as a top coach was made during a four-year spell at Chelsea - when he was under Jose Mourinho.
The 47-year-old remained at the west London club following the Portuguese manager's departure and served under Avram Grant before working in a similar role under Luiz Felipe Scolari.
He then left to join the Hammers, and has now chosen to accept a job as the first-team coach of Liverpool.
"Steve is a great addition to our backroom team and I'm delighted we've been able to bring him into the club," manager Kenny Dalglish said on the club's official website.
"I am looking forward to working with Steve alongside Sammy [Lee] and our other technical staff."