The Norwegian was put in temporary charge of the Lionesses after Phil Neville stepped down as boss in January, and subsequently oversaw a 6-0 win against Northern Ireland in a friendly at St George’s Park last month.
During her playing career, Riise helped Norway win Olympic gold at the 2000 Games in Sydney, and she was United States assistant boss when they were crowned champions at London 2012.
Riise will be assisted by former Canada international Rhian Wilkinson, who has been working alongside her in the England set-up, with a further coach to be announced in due course, the FA said.
Riise said in a statement from the FA: “I know first-hand as a former player just how huge the Olympics are as a tournament and I am enormously proud to have this opportunity to lead the GB squad into the Games.
“We will go there to give everything we have to be successful and I hope we can also use the power of the Games to help women’s football continue to grow in popularity.”
Baroness Sue Campbell, the FA’s director of women’s football, said: “We could not have been more impressed with the impact that Hege and Rhian have had in such a short space of time with England Women, particularly during our recent international camp at St. George’s Park.
“I am in no doubt that their Olympic experience and management expertise will provide the squad with the best possible opportunity to succeed at the Tokyo Games.”
GB will be among 12 teams taking part in the tournament at the rearranged Tokyo Olympics, with matches taking place between July 21 and August 6. They will learn who they will face when the draw is made on April 21.
Nine other competing nations have been confirmed so far in Australia, Brazil, Canada, Japan, Holland, New Zealand, Sweden, the United States and Zambia.
Neville had been in line for the GB job before he left his England role in January to take charge at Major League Soccer outfit Inter Miami.
Riise is England’s interim head coach ahead of Holland boss Sarina Wiegman taking the reins on a permanent basis in September.
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