"He has left because of the situation prevailing in Burundi," Tanzanian government spokesman Salva Rweyemamu told AFP, adding that Nkurunziza was heading back to the Burundi capital Bujumbura.
Meanwhile, the Burundian general who launched the coup ordered the closure of Bujumbura airport and land borders.
"I order the closure of the airport and border, and I ask every citizen and law enforcement down to the airport to protect it," General Godefroid Niyombare said in the radio broadcast.
East African leaders condemned the attempted coup.
"The summit condemns the coup in Burundi, it does not solve problems in Burundi," Tanzanian President Jakaya Kikwete said at the end of the day-long crisis meeting of the five-nation East African Community (EAC) -- made up of Kenya, Rwanda, Tanzania and Uganda as well as Burundi.
"We call upon the return to the constitutional order," Kikwete added, speaking in Tanzania's coastal city of Dar es Salaam.
"Given the situation in Burundi conditions are not conducive for elections in Burundi, and the summit calls upon the authorities to postpone the elections for a period not beyond the mandate of the current government."
Over 20 people have been killed and scores wounded since late April, when Burundi's ruling party nominated President Nkurunziza to stand for a third term on June 26, triggering daily protests.
Violence in Burundi has raised fears of a return to violence in the central African state, which is still recovering from a brutal 13-year civil war that ended in 2006.
Critics say a third term for Nkurunziza runs counter to both the constitution and the Arusha accords that ended the war.
The summit calls for elections "in respect of the constitution, the electoral law and the spirit of the Arusha peace agreement," Kikwete added.
Over 50,000 Burundians have fled into neighbouring nations since the unrest began.