Turkmen President Gurbanguly Berdymukhammedov earlier told Russian Prime Minister Vladimir Putin that his country would send four of the animals to Russia. One has already been caught.
Leopards used to live throughout the Caucasus region, but largely disappeared in the 1960s due to loss of habitat through urban expansion. Only a few leopards now inhabit the area. However, larger numbers can be still found in the Central Asian region, including Turkmenistan.
"The leopard avoids humans and is known for being able to hide even on open territory. It is not aggressive, and runs away from people," the coordinator for WWF projects in Turkmenistan, Viktor Lukarevsky said.
The return of the leopard to the Caucasus is the first major WWF-Russia conservation project sponsored by Russian businesses.