The female has taken up residence at the Loch of the Lowes centre near Dunkeld, which was home to Lady, thought to be the world's oldest breeding raptor, for 24 years.
A stringent protection programme is put in place once eggs are laid at an osprey nest.
The Loch of the Lowes nest is being monitored around the clock.
Staff at Loch of the Lowes fear former resident Lady may be dead, after she failed to return to the nest for the first time in a quarter of a century.
The venerable osprey, who would be 30 this year, laid almost 70 eggs and reared 50 chicks at the reserve.
Her mate of recent years, known as Laddie, has mated with the new female, and the pair united to chase off two other female intruders which had tried to move in to the area.
Scottish Wildlife Trust ranger Charlotte Fleming said there was "plenty of excitement" at the centre as the new female laid her first egg.
She said: "Now there is an egg on the nest, the osprey protection programme will begin in earnest. The Trust operates a 24-hour watch on the nest site to ensure the safety of the birds and the egg.
"Hopefully in the coming days there will be more eggs, as ospreys can lay up to four in a season."
The Trust operates a live webcam at the nest, which attracted more than a million viewers from 96 different countries last year.

Inspired by the lily pond in Monet's garden at Giverny in France, the painting was the top lot at Sotheby's sale of modern and impressionist works.
It totalled just under £122m, including £15.2m for Piet Mondrian's 1927 Composition with Red, Blue and Grey.
Sotheby's said it proved collectors are still keen to acquire "trophy art".
Paintings by Sisley, Picasso, Manet and Kandinsky were also among the 46 works, with only four pieces failing to find buyers as many sold close to the top end of the pre-auction estimates and sometimes above.
"The Nympheas selling for such a huge sum is again a reflection that this is still a market that is driven by trophies, that the great works by the major masters are still really sought after," said Philip Hook from Sotheby's.
The auction house said the bidding for the Monet work attracted buyers from Asia and all over the world and went on for 10 minutes, going up in £250,000 increments in its final stages.
It said the painting, from the "most iconic and celebrated of Monet's painting series, can be counted among the artist's greatest achievements".
It once belonged to Paul Durand-Ruel, the legendary art dealer who championed the Impressionists and represented Monet.
The same work had been offered for auction in 2010 but failed to reach its reserve price. Sotheby's said this time it had carried a more "realistic" estimate of £20m to £30m.
The sale price of £31.7m included a buyer's premium.
Two other Monet paintings were also offered in the sale, La Seine a Argenteuil which sold for £8.5m and Antibes, vue du plateau Notre-Dame, which sold for £7.9m.
A new female osprey which has nested at a Scottish Wildlife Trust reserve in Perthshire has laid her first egg.
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A 1906 Claude Monet water lilies painting, Nympheas, has sold for £31.7m in London, the second highest price ever paid for the artist at an auction.