This photo shows one of the birds with the other hidden.
Keith Betton, county recorder and chair of Hampshire Ornithological Society, said that they hatched overnight (April 20/21).
"The first two Peregrine chicks have hatched overnight and here you can see one with the other hidden," he said.
"The other two eggs should hatch today or tomorrow. Winnie had been very edgy for the last day and that will have been because the chicks start calling from inside the unhatched eggs in the day before they are about to break free. "Chester has also been around a lot so he will have been aware of the changes. Winnie has been eating the empty eggshells to get rid of them - but it also provides her with useful calcium.