Street, who was appointed head coach of the national side in 2007, led England to five consecutive Six Nations championship victories, including four Grand Slams and two World Cup finals.
England won the 2014 World Cup after a 21-9 win over Canada in Paris to lift the trophy for the first time in 20 years.
"Looking ahead to the 2017 women's rugby World Cup it was felt by all parties that a change would be beneficial to take the women's programme, which has evolved significantly in recent years, to the next stage," the RFU said in a statement.
Graham Smith, the team's assistant coach, will also leave his position following the end of this season's Six Nations campaign.
Nicky Ponsford will take interim charge during the Six Nations.
(Reporting By Michael Hann, editing by Alan Baldwin)
