Surveys from May and July this year, along with long-term observations, found that there were about 40 groups of beavers and seven dams in the Tay catchments.
The Tayside beavers have been in the area since at least 2006, and are thought to originate either from escapes or deliberate releases from private collections.
The Minister for the Environment decided in March this year to allow the Tayside beavers to remain in the wild until the Scottish Government decision on beaver reintroduction in 2015. Until then, the Minister has asked the Tayside Beaver Study Group (TBSG) to monitor and study the Tayside population.
The decision to reintroduce beavers to Scotland will be taken by the Minister for Environment and Climate Change, based on the information gathered from the Knapdale trial, as well as on various studies undertaken by the TBSG.
In response to concerns from farmers and other land managers in the area about dam building, the SNH report recommends measures such as installing devices to control water flow at problem beaver dams, protecting large and valuable trees next to rivers, and protecting lodges from being washed away to keep beaver construction activities to a minimum.
David Bale, chair of the TBSG said: "For the first time, we have a clear picture of how many beavers there are and how far they have spread.
"As the beavers are in an area with both farming and fishing, this is a good chance to see how beavers may affect land use.
"We encourage land managers to contact the TBSG if they have any issues with the beavers on their land."
Ian Mackintosh, of NFU Scotland, added: "The next two years must be used to provide the study group with evidence as to the lifestyle and habits of the beavers and their relationship to other land uses in the area.
"It's also important to gather as much detail as possible on the health status of the animals to ascertain if they are harbouring any diseases which might be difficult to control."
United Auctions had 4797 prime lambs forward at their Christmas show and sale at Stirling on Thursday. Top prices on the day were £96 per head and 213p per kg with the overall average levelling at 146.9p (+8.9p on the week).
The Cumberland and Dumfriesshire Farmers Mart sold 5173 prime lambs in Longtown on Thursday to a top of £92 and 237p to average 150.2p.
An extremely large show of 8254 cast sheep saw heavy ewes sell to £130.50 for Texels and average £63.04, while light ewes peaked at £74.50 for Cheviots and levelled at £37.44.
Cast rams sold to £120.50 for a Charollais and averaged £77.27.