Iraq's foreign minister had said in May that Qatar would open an embassy in Baghdad.
Qatari state media as well as Qatar-owned Al Jazeera said on their websites that Sheikh Tamim bin Hamad al-Thani had issued a decree appointing Zayed al-Khayareen as Qatar's "ambassador extraordinary and plenipotentiary to Iraq".
Tensions between the Sunni Muslim-ruled states of the Gulf and Iraq, which has a Shi'ite majority, have eased since Prime Minister Haider Abadi took office last year.
A rapprochement could help strengthen a regional alliance against Islamic State militants who have seized vast areas in both Iraq and neighboring Syria.
Saudi Arabia also signaled its intention to reopen an embassy in Baghdad earlier this year and has invited Abadi to visit the kingdom.
Some Gulf States have viewed Iraq as being too close to their main regional rival, Shi'ite power Iran.
Abadi's predecessor, Nouri al-Maliki, had accused both Qatar and Saudi Arabia of funding Islamic State insurgents, allegations denied by both countries.
Iraq recalled its ambassador to Qatar this week after the foreign ministry denounced a conference hosted by Doha it said included attendees wanted by Iraqi courts on terrorism charges.