The male and female were taken from Scotland to live in Cropton Forest, near Pickering in the North York Moors, a part of a managed re-introduction programme.
They were released in April 2019 at the Forestry England-owned site and have since settled in so well that they had two babies, known as kits, that summer.
It is the first time beavers have lived in the wild in Yorkshire since the 16th century.
One of the aims of the programme is to encourage natural flood management by enticing the beavers to build dams. In Cropton Forest, there are already several artificial dams to protect nearby homes.
Beaver monitoring projects around the UK reported that the animals' activities in areas where they had been re-introduced had helped to mitigate the effects of Storm Ciara and Storm Dennis this month. Their dams trap water and slow down the flow downstream, preventing a deluge.
In Cropton Forest, the pair have built a large dam and helped to reconnect the river with its floodplain.
Foresty England ecologist for Yorkshire Cath Bashforth said: “The beavers have been busy and made a large dam in the river. They have also fixed ‘leaks’ in ponds that were already there, meaning that more water is being stored in them. Their activity has definitely made a difference to how the water moves through the enclosure. The dam appears to be reconnecting the river to its floodplain and we are collecting detailed information on how this is slowing the flow. It is too early to say what impact the beavers have had on reducing flooding downstream.”
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.