Armenia agreed to hand over three districts around Karabakh – Aghdam, Lachin and Kalbajar – as part of the Russia-brokered deal in early November that stopped the fighting in the Karabakh region.
Azerbaijani forces have entered the Lachin district, the last of three handed back by Armenia as part of a deal that ended weeks of fighting over Nagorno-Karabakh.
The defence ministry in Baku said in a statement on Monday that "units of the Azerbaijan army entered the Lachin region on December 1" under the deal signed in early November by Armenia, Azerbaijan and Russia.
It released a video showing a tank flying the Azerbaijani flag and leading a column of trucks into the district along a road at night.
Aghdam was ceded on November 20 and Kalbajar on November 25.
The peace deal saw some 2,000 Russian peacekeepers deployed between the two sides including along the Lachin corridor, a 60-kilometre (35-mile) route through the district that connects Karabakh's main city Khankendi and the Armenian border to the south.
Clashes over Nagorno-Karabakh broke out between the ex-Soviet rivals in late September, reigniting the long-simmering conflict over the mountainous region.
The peace deal was reached after six weeks of heavy fighting that saw Azerbaijan's military overwhelm Armenian occupying forces and threatening to advance on Khankendi.
Under the agreement Armenia is losing control of seven regions occupied during the post-Soviet war in the 1990s, which killed 30,000 people and displaced many Azerbaijanis who used to live in the area.
The Armenian forces are retaining control over most of Karabakh's Soviet-era territory though they have lost the key town of Shusha.
Residents of Lachin cleared out frantically ahead of the handover, taking with them livestock, firewood, furniture, even plastic water pipes.
Some residents have also been burning their homes before they leave, and on Monday evening AFP journalists saw two houses on the outskirts of the town of Lachin in flames, sending clouds of thick smoke into the air.