The government, which took Mekelle in November after rebels rejected political reforms and captured army bases, has now called a “humanitarian ceasefire” in the region.
The fighting has left thousands dead and has pushed 350,000 towards famine with more than two million people have been displaced.
There had been recent reports of renewed fighting between fighters of the Tigray People’s Liberation Front (TPLF) and government forces outside Mekelle.
But a rapid offensive on Monday led to the unexpected recapture of the city by the rebels, in what may be a possible turning point in the bitter conflict.
A statement released by what was termed the Government of the National State of Tigray praised a “stunning victory”, saying Mekelle was “now under the complete control of the Tigray Defence Forces”.
It calls on the people and rebel forces “to stay vigilant, relentless and on constant alert until Tigray is fully free of all invading forces”.
The official said the interim government had decided to leave after rebels closed in “on every side”, adding: “Everybody has left. The last ones left in the afternoon… The region doesn’t have a government.”
Ethiopia’s government has yet to comment on any withdrawal and said that it was calling a military ceasefire for humanitarian reasons. It pointed to the need for aid workers to gain access, for farmers to get help during the planting season and for the return of internally displaced people.
Ethiopia’s government launched an offensive against the rebels last November. The TPLF had fallen out with the prime minister over political changes to the country’s ethnically based federal system and had taken over military bases in Tigray.
Ethiopia was aided by troops from neighbouring Eritrea, and their current status in Tigray remains unclear and all sides have been accused of carrying out mass killings and human rights violations.
Mr Abiy, a Nobel Peace Prize winner, declared that the conflict was over at the end of November, but fighting continued and flared ahead of parliamentary elections on 21 June.
The results of the elections, boycotted by some opposition groups and not held in some regions, including Tigray, are yet to be announced but are expected to favour Mr Abiy.
Earlier this month, the UN described a situation of famine in northern Ethiopia. It said the food situation had reached the level of a “catastrophe”, which it defines as starvation and death affecting small groups of people spread over large areas.
The UN’s World Food Programme (WFP), Food and Agriculture Organization and Unicef have all called for urgent action.
But the analysis was not endorsed by Ethiopia’s government, which has denied that there is a famine in the country.