The two beavers were released into Cropton Forest, near Pickering, in April as part of a project to assess the impact of their dam-building on the environment.
Video captured at the site by Forestry England has revealed that the pair have had two offspring, known as kits, who are already swimming.
Watch the moment wild beavers are released into the wild in Yorkshire for the first time in 400 yearsIt's not known what will happen when the kits reach breeding age themselves, as there are no other beavers living in the area.
Ecologist Cath Bashforth said:-
“We are all very happy to see the arrival of two healthy kits. With beaver being very social animals, the family unit will live together.
Why Saltaire became one of Yorkshire's coolest places to live“It is fascinating to watch them explore their surroundings and they are quickly learning from their parents. I’m really looking forward to watching them grow and bond as a family."
By 1900, there were few wild beavers left in Europe, and their population had been decimated by hunting. Conservation efforts have seen them gradually re-introduced.
The Cropton Forest beavers were transferred from a colony in Scotland for the flood management trial, which will monitor whether their activity has an impact on the artificial wooden dams in the area.
Iron Age remains could lie beneath Yorkshire field earmarked for 400 new housesTheir new home is a 10-hectare forest with 824 metres of beck and two old ornamental fish ponds, as well as young birch woodland and open areas for summer grazing.
Staff from Flamingo Land theme park helped with the transport and release of the animals.
Beavers were hunted for their fur and wild populations in Britain had been wiped out by the 16th century.
In 2009, four beaver families were relocated from Norway to Knapdale in Argyll, Scotland, and released into the wild.