The exchange was expected to involve the release by Azerbaijan of 32 Armenians mostly captured in late 2020. In return, Armenia handed over two Azerbaijani soldiers held since April 2023, Reuters reported.
Earlier on Wednesday, Russia's TASS news agency reported that Armenia and Azerbaijan were also discussing the withdrawal of troops from their shared border, though no decision had yet been taken.
The South Caucasus neighbors have fought two wars in the past 30 years over Nagorno-Karabakh, a mountainous area that is part of Azerbaijan, but where ethnic Armenians had broken away and established de facto independence in the 1990s.
Azerbaijan recaptured Karabakh in a lightning offensive in September, prompting most of its 120,000 ethnic Armenians to flee to Armenia.
Announcing the planned prisoner exchange last week, the two sides said they "reconfirm their intention to normalize relations and to reach a peace treaty on the basis of respect for the principles of sovereignty and territorial integrity".
The agreement was welcomed by the European Union and the United States, which have tried for decades to persuade the two countries to sign a peace treaty to settle outstanding issues including the demarcation of their borders.
Armenia and Azerbaijan were both part of the Soviet Union, which collapsed in 1991.