A Brazilian air force plane was waiting to fly him away on Sunday after Quito's Congress voted to remove Gutierrez from office following a week of street protests.
Ecuador's unrecognised new government said on Friday it would let the ousted president go, although Brasilia said it would only fly Gutierrez in when safe passage from the ambassador's residence to the airport was guaranteed.
Quito had been dragging its feet on granting permission, apparently fearing the reaction of Ecuadoreans outraged that Gutierrez will not be tried for alleged abuse of power, corruption and repression of peaceful protests.
The political crisis was the latest in a long history of political instability in the South American country of 12.5 million people.
Since 1997, three presidents have been driven from office in Ecuador before completing their terms.
More than 1000 Gutierrez loyalists took to the streets in his hometown of Tena on Saturday, protesting against the new government and calling his ouster illegal, police in the remote Amazonian town said.
Lucio Gutierrez was granted
asylum in neighbouring Brazil
Police said the peaceful rally was led by the ousted leader's brother, Gilmar Gutierrez, along with the town mayor and others in Gutierrez's Patriotic Society party.
And Gutierrez, a 48-year-old cashiered army colonel elected in 2002, has said the congressional vote that removed him from office violated the constitution.
In a resolution on Friday, the Organisation of American States avoided explicit recognition of the government of President Alfredo Palacio - who was sworn in by Congress on Wednesday after it removed Gutierrez.
It was not known when the OAS delegation would arrive. So far no country has recognised the new government as legitimate.
Congress justified dismissing Gutierrez under a constitutional clause allowing lawmakers to remove a president for "abandonment of the post", even though he was still in the Government Palace issuing orders.
Backers of the measure argued since Gutierrez had not faithfully carried out his responsibilities, Congress should declare the presidency vacant.