Slutsky had first offered to step down on Monday after a 3-0 defeat to Wales.
His resignation has now been accepted by the Russia Football Union (RFS), the Tass news agency reported.
Sports Minister Vitaly Mutko, who is also RFS president, said Slutsky would now focus on coaching CSKA Moscow.
Slutsky had coached both the national team and CSKA after his appointment to succeed Italy's Fabio Capello as Russia coach in August 2015.
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"We will deal with the issue on searching for the new head coach starting from today," Mutko was quoted by Tass as saying.
Russia finished bottom in Group B, drawing 1-1 with England but losing 2-1 to Slovakia before the drubbing by Wales.
