The 47-year-old formed part of Eriksson's staff at the London 2012 Paralympics as the nation finished third in the athletics medal table with a total of 29 - 11 gold, seven silver and 11 bronze.
But she will now take over full responsibility of Britain's athletes following Eriksson's decision to leave the post in order to replace Charles van Commenee as head coach of non-disabled team last month.
Under Eriksson, who was first hired by UK Athletics in 2009, Britain won 38 medals, including 12 golds, at the World Championships in New Zealand 2011 before securing 29 at London 2012.
Dunn, a former sprinter who won medals at the European Championships and Commonwealth Games, is UK Athletics' first female head coach and she wants to keep such successes going.
"London had an amazing impact on Paralympic sport in the UK and we have a real opportunity to build on that over the next four years," said Dunn. "I'm looking forward to unearthing more talent and building on that success.
"Working closely with Peter over the past four years has been superb, but I am looking forward to taking the reins and continuing what is, in effect, a long-term plan to see further medal success in Rio in 2016.
"As a former European and Commonwealth Games medallist, I know the commitment, passion and sheer determination it takes to achieve the very best. I have used this experience to develop some of the best Paralympic athletes in the world and I can't wait to take the team to the next level."