The eggs are in a nest on the ledge of the Newton Building at Nottingham Trent University which is being filmed by a Nottinghamshire Wildlife Trust webcam.
A wildlife trust spokesman said the eggs were the first in the East Midlands so far this year.
Falcons have been nesting on the building for about 13 years, he said.
"It is always great news that a pair are back using the nest site - it is so important to have such a long successful nesting site," trust spokesman Erin McDaid said.
Peregrine falcons are a protected species and cannot be trapped or shot. A male peregrine falcon found dead at Derbyshire Wildlife Trust's headquarters in Belper earlier this year had been shot in the shoulder, tests revealed.
The Nottingham birds are the first in the East Midlands to lay, beating pairs nesting on cathedrals in Derby and Norwich, Mr McDaid said.
"We have had a huge level of interest on social media over the weekend so it looks like the pair will have a huge following again this year.
"It is great to see them back and see them using the nest. We just have our fingers crossed that the eggs haven't arrived too early."
Three chicks died on the same site in 2012 after severe cold weather.
Two peregrine falcon eggs have been spotted on the roof of a Nottingham building as the protected birds' breeding season begins.