Clarke's last job was as assistant toGianfranco Zola at West Ham but his reputation as a coach is built onfour years as assistant to Jose Mourinho at Chelsea.
Dalglish said: 'Steve is a great addition to our backroom team and I'm delighted we've been able to bringhim into the club.
Straight to work: Steve Clarke (left) watches on in training with Kenny Dalglish
'I am looking forward to working with Steve alongside Sammy and our other technical staff. It is important we have good backroom staff and Steve comes into that category.
'To be fair to Steve he was phoned last night and he was up here for training this morning - which tells you the lure Liverpool football club has to someone.
'He was very instrumental in the success of several clubs, none less so than Mourinho's spell at Chelsea so we've got a decent guy there. He worked well in tandem with Sammy this morning so it looks positive for us.'
Clarke added: 'I was sat at home doing nothing and now I've got the chance of working with a football great in Kenny Dalglish and also working for one of the world's leading football clubs.
'This was something I couldn't turn down. I am grateful for everybody who has given me such a warm welcome, especially all those here at Melwood. I am really looking forward to working with Kenny and the rest of the staff to help bring good times back to the club.'
Able deputy: Steve Clarke, who built his reputation as Jose Mourinho's right-hand man at Chelsea, is set to be named as new Liverpool coach
At Stamford Bridge he helped the Portuguese coach guide the Blues to their first league title in 50 years in 2005 before adding another Premier League the season after along with two League Cups and an FA Cup.
Clarke stayed on at Chelsea under Moruinho's successor Avram Grant and acted briefly as Luiz Felipe Scolari's right-hand man before leaving Chelsea in September 2008 for Upton Park to assist Gianfranco Zola in charge of the Hammers.
The 47-year-old has been out of work since he followed Zola out of West Ham last summer but is expected to be named Liverpool's new first team coach.
It is understood the Scot will replace Mike Kelly, the former Fulham coach, who is set to follow sacked boss Roy Hodgson out of Anfield.
Clarke began his duties at the club's Melwood training ground on Monday before taking a seat alongside Dalglish in the dug-out at Bloomfield Road for Liverpool's Barclays Premier League visit to Blackpool.
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Explore more:People: Gianfranco Zola, Mike Kelly, Kenny Dalglish, Roy Hodgson, Luiz Felipe Scolari, Jose Mourinho Places: Liverpool