The announcement came on Wednesday after a meeting between Armenian Prime Minister Nikol Pashinyan and Azerbaijan President Ilham Aliyev, Reuters news agency reports.
Pashinyan's secretariat says it has ordered its foreign ministers to begin preparations for formal peace talks.
They will also establish a joint commission that will determine where the border between the countries will go, the statement says.
The Commission will start work at the end of April.
The conflict has been going on since the late 1980s and concerns the Nagorno-Karabakh region, a part of Azerbaijan inhabited mainly by Armenians.
The local parliament decided in favor of joining Armenia, which was eventually followed by a war that ended in a loss for Azerbaijan.
When the ceasefire was concluded in 1994, Armenian forces had taken control of Nagorno-Karabakh, but also of a nearby part of Azerbaijan.
Russian mediation
In 2020, Azerbaijan withdrew with the support of Turkey and took over large parts of the lost territories.
At least 6,500 people were killed before the parties agreed to cease fire after Russian mediation.
Russia has since had nearly 2,000 peacekeepers in Nagorno-Karabakh, but according to unconfirmed Azerbaijani and Ukrainian sources, much of the force was withdrawn to contribute to the invasion war in Ukraine in early March.
At the end of March, Azerbaijan further advanced its positions.
Russia accused the country of violating the ceasefire agreement by taking control of parts of the zone for which Russia was responsible.