The spokeswoman for EU foreign affairs and security policy said he would officially leave the position on August 1.
“All the necessary steps are being taken to swiftly appoint a new ambassador,” Maja Kocijancic said.
The resignation comes at a sensitive time in EU-Turkish relations as the bloc recently brokered a deal with Turkey to curb illegal migration.
The agreement called for irregular migrants who arrived in the Greek islands from Turkey after March 20 to be sent back to Turkey.
The EU, in turn, is to resettle one Syrian refugee from Turkey to the bloc for each Syrian that Greece returns to Turkey.
Turkey also stands to receive up to six billion euro (£4.76 billion), visa-free travel and fast track negotiations on EU accession.
Visa-free travel to Europe, however, is conditioned on Turkey amending its anti-terrorism laws, among other criteria.
That requirement has proved a sticking point and the subject of sharp exchanges between EU and Turkish officials. Ankara argues that it cannot narrow its laws when it faces the twin threats of Islamic State and Kurdish rebels.
Turkish prime minister Binali Yildirim stressed that anti-terror laws would not be amended.
Brussels worries that the existing legislation is too sweeping and plays a role in restricting dissent and media freedoms.
Mr Haber had angered Turkish government officials last month after he criticised Turkey’s reluctance to meet the remaining criteria for the visa-free deal, and reportedly quoted a German expression, “to start like a Turk and finish like a German”.
He was summoned to Turkey’s foreign ministry and asked to explain his words, which evoked negative cultural stereotypes.
Mr Haber was previously posted in Ankara between 1993 and 1996 as a German diplomat. He returned as head of the EU delegation to Ankara in September 2015.