Heimir Hallgrimsson, 46, has worked as the number two since 2012 but will take over on his own at the end of the team's Euro 2016 qualifying campaign, the 65-year-old Lagerback told a news conference on Monday.
Iceland finished second in their 2014 World Cup qualifying group and missed out on a place in the finals at the playoffs earlier this month.
Goals from Mario Mandzukic and Darijo Srna gave Croatia a 2-0 victory in the second leg, and on aggregate, in Zurich last Tuesday.
Iceland have never reached the finals of a major tournament.
(Editing by Tony Jimenez)
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