Staff at the Scottish Wildlife Trust's Loch of the Lowes Wildlife Reserve, in Perthshire, saw the first signs of hatching just after midnight on Wednesday, however the chick did not fully hatch until around 1.15am on Thursday.
It comes after the first chick of the season broke out of its egg just before 10pm on Monday, hatching fully by the early hours of Tuesday.
By 3am on Thursday, both chicks could be seen in the nest, and a few hours later they received a beakful of fish from their mother NC0.
She laid three eggs in the nest and it is hoped the third will hatch soon.
This season is the second as a breeding pair for NC0 and male osprey LM12, after they successfully fledged one chick last year.
Hayley Hodgson, species protection officer at the trust, said: "Compared to the first chick this one took its time coming out of the egg, but we're delighted there are now two young ospreys in the nest. Hopefully it won't be long until the third hatches out.
"Since they hatched both chicks have been regularly fed, thanks to the strong teamwork of their parents. LM12 is regularly bringing fish to the nest and NC0 is diligently offering up pieces of fish to her youngsters.
"Thanks to support from our staff, volunteers and players of People's Postcode Lottery, our season is progressing really well.
"The best way to follow the progress of the chicks is to watch our live webcam, or book a ticket online for our visitor centre."
Ospreys were extinct in Britain for much of the 20th century but began to recover in the 1960s and today an estimated 300 pairs breed in the UK each summer.
The trust's Osprey Protection Programme is supported by players of the People's Postcode Lottery.
Laura Chow, head of charities at lottery, said: "I'm thrilled that a second chick has hatched out at Loch of the Lowes and we're pleased that support from players of People's Postcode Lottery is contributing to another successful breeding season at the reserve.
"We'll be keeping our fingers crossed that the third chick will emerge soon."