Despite beating neighbours Denmark in a playoff to reach the finals, Hamren had been expected to quit after the tournament, with Sweden failing to make the 2014 World Cup and finishing third in their Euro qualifying group behind Austria and Russia.
"He has given us a decision that he is going to step down," FA vice-chairman Lars-Christer Olsson told state broadcaster SVT on Monday.
Hamren, who took over from Lars Lagerback in 2009, will take charge of the side when they open their Euro 2016 campaign against Ireland at Stade de France on June 13, before further Group E matches against Italy and Belgium.
(Reporting by Philip O'Connor; Editing by John O'Brien)
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