Having narrowly missed out on the 2014 World Cup in Brazil, 67-year-old Lagerback led Iceland to the finals of a major tournament for the first time.
The Swede, who has coached his native country and Nigeria at international level, had previously indicated that he would step down at the end of the European Championship but confirmed the decision after naming his squad.
"It was a very hard decision, I have to admit I haven't gotten any younger," he told reporters.
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"But the main reason is that maybe I should do something else with friends and family."
Not known for being sentimental, Lagerback included Iceland's record goalscorer Gudjohnsen in his squad for France on the back of the striker's strong performances for Norwegian side Molde.
The former Chelsea and Barcelona forward has only scored one goal in seven games for Molde but has been praised by coach Ole Gunnar Solskjaer for his work rate and experience.
Iceland will face Portugal, Hungary and Austria in Group F at Euro 2016 which starts next month.

Squad in full:

Goalkeepers: Hannes Þór Halldórsson, Ögmundur Kristinsson and Ingvar Jónsson.
Defenders: Ari Freyr Skúlason, Hörður Björgvin Magnússon, Hjörtur Hermannsson, Ragnar Sigurðsson, Kári Árnason, Sverrir Ingi Ingason, Birkir Már Sævarsson and Haukur Heiðar Hauksson.
Midfielders: Emil Hallfreðsson, Gylfi Þór Sigurðsson, Aron Einar Gunnarsson, Theodór Elmar Bjarnason, Arnór Ingvi Traustason, Birkir Bjarnason, Jóhann Berg Guðmundsson, Eiður Smári Guðjohnsen and Rúnar Már Sigurjónsson.
Forwards: Kolbeinn Sigþórsson, Alfreð Finnbogason and Jón Daði Böðvarsson.
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