Dalglish adds Clarke to Liverpool staff
Clarke was Jose Mourinho's assistant at Chelsea and most recently performed a similar role with Gianfranco Zola at West Ham United.
"Steve is a great addition to our backroom team and I'm delighted we've been able to bring him to the club," Dalglish told Liverpool's website.
"I am looking forward to working with Steve alongside Sammy (Lee) and our other technical staff."
Dalglish was appointed caretaker manager on Saturday after Roy Hodgson's disappointing six months in charge came to an end.
The Scot, who won virtually every major honour with Liverpool in a 14-year stint as player and then coach after joining from Celtic in 1977, lost his first game since stepping back into the hot seat on Sunday as Liverpool went out of the FA Cup 1-0 at Manchester United.
Liverpool languish in 12th place in the Premier League, just four points off the relegation zone, and face Blackpool in a re-arranged fixture on Wednesday.