Monty and Glesni were sitting on the eggs in their nest in the Dyfi Valley, near Machynlleth.
The first chick hatched at around 11:00 BST on Saturday but it is too early for wildlife experts to tell if it is a male or female.
Monty produced two chicks, Cerist and Clarach, with Glesni in 2013.
He has returned to breed at the Montgomeryshire Wildlife Trust site at Cors Dyfi every year since 2011.
His previous partner, Nora, failed to return from Africa in spring last year.
A spokesman for the Dyfi Osprey Project said: "It is the day we have been waiting for.
"We spotted a tiny crack in the egg and the chick emerged a few hours later. There was hardly a dry eye in the house."
The birds of prey are kept under constant watch at the nesting site where a webcam films their every moment.
They are the only breeding pair of ospreys that can be visited by the public in Wales. A pair has also bred in the Glaslyn Valley, near Porthmadog, since 2004.
A pair of rare ospreys in Powys have become parents again after one of their two eggs hatched.