The news that President Compaore had stepped down after 27 years in office was first announced by an officer at the military headquarters in the capital, Ouagadougou on Friday.
"As of today, Compaore is no longer in power," Colonel Boureima Farta told thousands of protesters outside of the headquarters.
The announcement was met with cheers from the crowd who had been protesting to demand that the president step down immediately.
A few minutes later, the now former president released a statement confirming that he had resigned.
Earlier on Friday, thousands of demonstrators were reported to be back on the streets of the capital, a day after thousands of people, including soldiers, took part in a demonstration which culminated with some storming the parliament building.
The military briefly imposed martial law in an effort to restore order, while at the same time saying it had dissolved parliament and would appoint an interim government, in which all major political parties would be represented.
Late on Thursday, the president again rejected the calls for his immediate resignation, saying he would remain in office for another year.
"With regard to myself, I am available to open talks on a transitional period at the end of which I will hand over power," Compaore said in the statement broadcast on BF1 TV.
The president also confirmed that he had abandoned an effort to amend the constitution in order to allow him to run for a fifth term in office - a plan that had angered many and sparked the street protests, which began on Tuesday.
Compaore led Burkina Faso since taking power in a 1987 coup. He has been elected four times since then, but the opposition has disputed the results.
In Friday's statement, Compaore declared that Burkina Faso was currently in a "power vacuum" and he called for "free and transparent" elections within the next 90 days.
pfd/kms (AFP, dpa, Reuters, AP)