Hamrén made the formal announcement at a press conference on Monday afternoon, after sports website Fotbollskanalen broke the story earlier in the morning.
"I have decided to quit as coach when my contract runs out after the Euro 2016 in France this summer," he told reporters.
Hamrén took the reins of the national team from Lars Lagerbäck in autumn 2009, who stepped down after Sweden failed to qualify for the World Championships in South Africa.
But he too faced criticism after Sweden performed worse than expected in the Euro qualifiers last year, only ending up third in its group behind Austria and Russia. However his contract was automatically extended for the summer after the team eventually managed to clinch a place in the finals.
His legacy will likely be measured in terms of how well Sweden perform in France. But they are expected to face a tough challenge, after being drawn in a group comprising of Italy, Belgium and the Republic of Ireland.
Their first game will be against Ireland on June 13th in Saint-Denis, then Italy in Toulouse on June 17th and finally Belgium in Nice on June 22nd. The top two teams from each group qualify for the knock-out stages of the competition.
The Swedish Football Association did not want to comment on who could take over after Hamrén. However, names that have previously been linked to the position are Helsingborg FF's manager, and former national footballer and Celtic legend, Henrik Larsson; Håkan Ericson, who is currently in charge of the U21 national team; new Denmark coach Åge Hareide and IFK Gothenburg coach Jörgen Lennartsson.