All four nesting pairs of the flightless birds bore children within a few days of each other.
The babies have been named after nuts, and it marks a 100 per cent success rate for this year’s clutch.
Marwell Zoo senior bird keeper, Christopher Kent, said: ‘Initially the new chicks will have their natal down feathers (which are visible at the moment) but as they grow they will go through several moult phases to get them waterproof and able to swim.
‘Their final immature plumage is a pale grey, being lighter on the underbelly, but not clearly defined like the adults.’
Footage shows the moment one of the chicks was born.
All four of them, Peanut, Pistachio, Cashew and Macadamia, are expected to stay in their burrows for approximately 12 weeks.
Their parents will take turns to feed them and watch the nest.
Jupiter and Billie’s chick, Peanut hatched on April 27.
Pistachio was born three days later, from Lurch and Calippo, with Macadamia entering the world on May 5, in Lucy and Buddy’s nest.
Cashew was the last birth, from Jacko and Lilly, on May 8.
Humboldt penguins are listed as vulnerable to extinction, and are native to the coasts of Peru and Chile.
Mr Kent added: ‘There will be lots of feeding and maybe a bit of squabbling to see amongst the colony, but this is all natural behaviour that we expect, especially with a bumper number of chicks this year.’