The mammals were introduced into Cropton Forest in the North York Moors, after being moved from Scotland earlier this year.
Forestry England initiated the move as part of a five-year trial to combat flooding, curious to see how they interact with man-made dams.
Since then, hidden cameras have captured the two with two babies, known as kits, swimming and interacting with one another.
Cath Bashforth, ecologist at Forestry England, said: "We are all very happy to see the arrival of two healthy kits.
"With beavers being very social animals, the family unit will live together. 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."
Beaver dams have been proven to bring huge environmental benefits to ecosystems as they create large areas of water-retaining wetlands, thus reducing downstream flooding.
The move to Cropton Forest was licensed by Scottish Natural Heritage, and follows two decades of flooding in the area. One flood in 2007 caused £7m of damage o homes and businesses.
Forestry England described the move as "a revolutionary trial in natural flood management" adding that they hoped the beavers would maintain existing man-made dams and create their own, potentially reducing the impact of flooding locally.
It is also expected that the beavers' activity in Cropton Forest will improve biodiversity in their 10-hectare home.
The animals will be monitored throughout the five-year project to assess the benefits they bring to the ecosystem.