The otters were five weeks old when they were found in October, with rescuers reporting seeing the mother leave the holt after the tree had fallen.
Dave Webb, from the otter trust, said at the time she may have been “spooked” by the fall, and said the cubs were in “immediate danger” when she did not return the next day.
Compton Verney said the cubs are now weaned and settling in to the rehab centre.
The post said: “We can confirm that Snap and Crackle are both male and Pop is female.
“At the time of their rescue, Pop weighed under 300 grams and was the smallest cub the trust had ever looked after.”
Otters have been present at Compton Verney since 2020, but this is the first confirmed breeding on site.
The art gallery added: “Thanks to swift action from the grounds team here at Compton Verney and the commitment and expertise of the team at the otter trust, the three siblings are going from strength to strength.
“Fingers crossed they can make a safe return to Compton Verney in the autumn.”