Diendere, a former spy chief, was at the head of a week-long power-grab by Burkina Faso's powerful presidential guard last month, during which the interim president and prime minister were held hostage.
He had sought sanctuary in the embassy in the recent days after the transitional government - tasked with guiding Burkina Faso to elections this month - was returned to power amid international pressure and popular protests.
"He has been handed over to Burkinabe authorities," said a judicial source close to the transitional government.
A military source said Jean Baptiste Ouedraogo, the former president of Burkina Faso, escorted the former putschist to the capital Ouagadougou's main gendarmerie camp in a heavily armed convoy.
Earlier, Prime Minister Yacouba Isaac Zida had said the government had provided guarantees to the Vatican embassy that Diendere's life would be respected if he was handed over. Zida said he would be handed to judicial authorities.
Diendere said he had led the coup because of proposals to dismantle the elite presidential guard, the RSP, and to exclude allies of deposed president Blaise Compaore from running in this month's scheduled presidential election.
The putsch lasted a week and the government was restored last Wednesday. During its first post-coup cabinet meeting it formally disbanded the RSP and launched an inquiry into the military power-grab.
The army's chief of staff on Monday accused Diendere and Compaore's former foreign minister Djibril Bassole of hindering attempts to disarm the elite unit and of seeking support from foreign forces and Islamist militants.
Bassole was arrested at his home on Tuesday.
Gendarmes on Thursday detained Mohamadou Djeri Maiga, the vice-president and chief negotiator for neighbouring Mali's Tuareg separatist National Movement for the Liberation of Azawad (MNLA) rebellion.
"He was detained to be questioned in relation to the current inquiry. It's related to the coup attempt," a Burkinabe security source told Reuters. "He was detained to be questioned. He wasn't arrested."
A spokesman for the Coordination of Azawad Movements (CMA), a grouping of five rebel movements including the MNLA, said Maiga was detained at the Ouagadougou airport as he prepared to fly to Bamako to sit on a committee monitoring a peace accord agreed earlier this year.