The female gentoo couple, Marama and Rocky, have been together for five years and adopted the egg after demonstrating to the aquarium's team that they would make good parents.
The egg was moved from its birth mother to relieve her of the pressure of raising two chicks.
The tiny bundle of fluff's name and gender has yet to be revealed.
General manager Graham McGrath said: "Marama and Rocky have taken to becoming parents like ducks to water - or should I say penguins.
"Caring for a newborn is tough for anyone, from the sleepless nights to the constant feeding, yet this wonderful pair of penguin parents are completely unflappable and seem to be taking it all in their stride."
Marama is the older of the pair and naturally more protective of the chick, while Rocky - who is free-spirited and inquisitive - is keen to teach the new arrival everything it needs to know about life as a penguin.
The new parents have built the biggest nest in the colony and each perform shifts, giving the other a chance to swim and feed.
Last week, penguins at ZSL London Zoo were photographed with an LGBTQ+ Pride banner to celebrate the annual parade.
Penguins are said to mate for life, and same-sex pairings have been observed both in the wild and in captivity.
The gentoo chick is the second to be born at Sea Life London this year, as part of its conservation programme.