Russia's military presence on the border with Ukraine has created great political tensions in recent times.
Russia is now announcing the withdrawal of troops.
The country's defense minister Sergei Shoigu said on Thursday that he had ordered the units involved in exercises in the areas to return to their bases on May 1.
- I believe that the goal of the assignment has been achieved.
The troops have demonstrated their ability to establish a defense for the country and I have therefore decided to end the exercises in the southern and western military districts, says Sergei Shoigu, reports Reuters.
"Welcome all steps"
According to a spokesman for Ukrainian President Volodymyr Zelensky, Russia has had more than 40,000 troops stationed on Ukraine's eastern border and more than 40,000 on the Crimean peninsula.
About 50,000 of them are said to have been sent there in the last month alone, writes Reuters.
"Ukraine welcomes all steps to reduce the military presence and calm the situation in the Donbas," Volodymyr Zelensky wrote on Twitter after the announcement.
He further writes that he is "grateful for the support of international partners".
Weapons are left behind
Russia has not yet confirmed any figures.
Earlier in the day, more than 10,000 soldiers and 40 warships had moved on the Crimean peninsula.
However, military equipment will be left near the city of Voronezh to be used in another planned exercise later this year, Reuters reports.
The announcement comes in the wake of President Vladimir Putin's speech on Wednesday in which he more or less Western countries for crossing an unspecified "red line".