Dalglish, 66, won eight league titles, three European Cups, two FA Cups and five League Cups during a glittering 13-year stint as a player and two managerial tenures.
The Kenny Dalglish Stand will be officially opened in a ceremony later this year.
"It is testament to Liverpool's history and status that we are not lacking in truly great individuals, whose names could easily grace a stand at Anfield," said principal owner John W Henry in a press release.
"But in Kenny Dalglish we have a person who carries such immense significance to the fabric of this club, so it feels somewhat incumbent on us to recognise this in a manner that is befitting to the man.
"His name is synonymous with our club, with our home and the city of Liverpool. Now it will be as visible as it is palpable."
As well as his role in Liverpool's golden era in the 1970s and 1980s, Dalglish also received plaudits for supporting victims' families after 96 fans died in the 1989 Hillsborough stadium disaster.
Anfield has two sets of gates dedicated to former managers – the (Bill) Shankly Gates and (Bob) Paisley Gates – but none of its stands currently carries the name of an individual.
"We recognise this won't sit comfortably with Kenny's default position of humility and self-deprecation, but as we approach the club's 125th anniversary year now is the right time in the club's illustrious history to leave this legacy," said chairman Tom Werner.
"For decades he has served the club and the city with the steadfast attitude that the collective always comes ahead of the individual."
The Centenary Stand sits across the pitch from Anfield's giant Main Stand, which was reopened last year after work to increase its capacity by 8,500 seats.
A unique honour for a unique man. pic.twitter.com/uiTYvlVSrO