The former West Ham and Fulham full-back joins the Championship club on a three-year deal after making just 18 appearances at Liverpool.
Speaking on Leicester's official website, manager Sven Goran Eriksson said: 'Paul has been a Premier League player year in and year out throughout his career so he represents a very big signing for us.
On the move: Konchesky has agreed a three-year deal with Championship outfit Leicester
'He wanted to come to Leicester City and it means a lot that proven, established top flight footballers want to be part of what we are building here.
'I know Paul very well as a player and as a person and he will be a top class addition to our squad.'
Dead wood: Jovanovic is set to follow Konchesky out of Anfield
Konchesky's departure is likely to be the first of several as Dalglish looks to shed some of the dead wood which has accumulated at Anfield.
Forward Milan Jovanovic, who arrived on a free transfer from Standard Liege last summer, is expected to be the next out of the door after scoring just twice in 18 matches.
The Serbia international started just one game under Dalglish and did not feature in the squad for the last three months of the season.
He may possibly return to Belgium with Anderlecht, although French champions Lille are believed to be interested in the 30-year-old.
Several other fringe players also seem set for the exit with 31-year-old midfielder Christian Poulsen and Joe Cole, 30 in November - both signings from the short-lived Hodgson era - linked with moves away.
Striker David Ngog appears to be surplus to requirements now and has been interesting some Barclays Premier League rivals, while the future of back-up goalkeeper Brad Jones appears in doubt with Liverpool apparently close to bringing in Roma's Brazilian Alexander Doni as Jose Reina's deputy.
Left-back Emiliano Insua, who spent last season on loan at Galatasaray, may have earned a reprieve, however, after he flew out to Malaysia yesterday to await the arrival of the first team squad, who play their first pre-season friendly against Guangzhou in China today.
The Argentinian did not get a visa for the China leg of the mini-tour but is hopeful of being involved against a Malaysia XI at the weekend. 'I will meet the team on Thursday. I am looking forward to playing on Saturday,' he wrote on Twitter.
Pompey and Wolves set to battle it out over Liverpool flop Konchesky Sven Goran Eriksson wants Paul Konchesky to help Leicester promotion bid