Zimbabwe Cricket (ZC) made the announcement on Wednesday but said Houghton, regarded as one of the country's most accomplished former players, would remain within the organisation in an as yet unspecified role.
In a resignation letter to the ZC board, Houghton said he had "lost the changeroom" after 18 months in charge and felt that a "new voice" was needed to take the team forward.
"While the past few months have been disappointing as we failed to qualify for both the 50-over World Cup and the T20 World Cup, they should not obscure all the work he (Houghton) has done over the past year to rebuild the foundations for long-term success," ZC chairman Tavengwa Mukuhlani said in a statement.
"Dave leaves the team with our sincerest thanks for his tireless efforts and we are looking forward to working with him in a different role as we seek to change our on-field fortunes."
An interim technical team will be named shortly for Zimbabwe's tour to Sri Lanka in January for a white-ball series.
The ZC board also appointed a three-member committee chaired by Lloyd Mhishi to probe the World Cup qualification failures as well as to review ZC's cricket affairs structure. The committee is to report back in three weeks.
