Also known as little blue penguins, little fairy penguins are blue-grey in colour and are native to New Zealand and Australia
Henry was the second of two eggs laid by proud parents Tyrion and Dandy, who are in their first breeding season as a couple.
The Sea Life Centre said the hatching was “a significant milestone” in its breeding programme.
It said Henry required “some gentle assistance” from the centre’s animal care team after struggling to break free from his shell.
Henry has taken to solid food immediately after his first feed, a positive sign that required no transition period with liquidised meals.
Henry brings the total number of little penguins at Weymouth to 42.
The colony was established in 2018 when 25 of the animals were moved from Australia.
The facility was the first in Europe to successfully breed the species.
Webster said: “Watching him break free from his shell, with a little helping hand from our animal care experts, was an incredibly special moment.
“Henry’s successful hatching is a wonderful testament to six years of dedicated breeding work here at Sea Life Weymouth.
“As Europe’s only little penguin colony, every new arrival is significant.”