jihadists demanding that France halt air strikes against the Islamic State group.
The body was found buried without its head in Akbil, where Gourdel was abducted by the Jund al-Khilafa (Soldiers of the Caliphate) group, the sources said.
The army had mobilised 3,000 troops to find the 55-year-old mountain guide's body and launched a new search operation on Wednesday.
Excavations were carried out in Akbil and the neighbouring town of Abu Youssef following a tip-off by an Islamist detainee, a security source told AFP.
The search was headed by an elite army unit and aided by sniffer dogs.
Police experts arrived at the burial site, located in a forested area known as Tabounecht Abu Youssef, that had been rigged with explosives, which a local resident said was aimed at "causing casualties among the searchers."
The military had to bring in munitions experts to sweep the area first, the source said.
Forensic experts were present to perform tests to formally identify the body, which was exhumed in the presence of Algeria's senior terrorism prosecutor and the judge presiding over Gourdel's case.
Gourdel was abducted by Jund al-Khilafa on September 21, while hiking in a national park that was once a draw for tourists but became a sanctuary for Islamists.
He was beheaded days later in a video posted online after France rejected the jihadists' demand to halt air strikes against the Islamic State group in Iraq and Syria.
Jund al-Khilafa had earlier pledged allegiance to IS.
In December, the army said it had killed the leader of the militants who beheaded Gourdel.
The body of Abdelmalek Gouri, who claimed responsibility for the Frenchman's killing, was identified after an operation in which two other suspected militants were killed in Isser, about 60 kilometres (40 miles) east of Algiers.
An Algerian court has also launched legal proceedings against 15 people suspected of participating in the beheading.
Gourdel's death followed calls by IS for Muslims to kill Westerners whose nations have joined a campaign to battle the jihadist group in Iraq and Syria.
Violence involving armed Islamists in Algeria has fallen considerably since the civil war of the 1990s, but groups linked to Al-Qaeda in the Islamic Maghreb continue to launch attacks in the northeast, mostly on security forces.Gouri, alias Khaled Abou Souleimane, was the former right-hand man of AQIM leader Abdelmalek Droukdel, and is suspected of helping to organise suicide attacks on the government palace and against a UN contingent in Algiers in 2007.
He is also thought to have masterminded an April attack that killed 11 soldiers in Iboudrarene, the same region where Gourdel was kidnapped.