Defence minister Sergei Shoigu said the teams would start to leave on Thursday, according to Interfax news agency.
Russia sent equipment and 100 soldiers in March as the outbreak threatened to overwhelm northern Italy.
The deployment provoked controversy in Italy, as many saw it as a big propaganda move by Russia and questioned its practical use.
However, Prime Minister Giuseppe Conte approved the operation - dubbed "From Russia With Love" by Moscow - after speaking with President Vladimir Putin.
Italy had been struggling to procure medical equipment and aid from neighbouring nations as deaths and new cases soared in March.
Members of the far-right League Party - which has repeatedly praised Russia in the past - called the support "precious" in the worst affected region, Lombardy. The Russian personnel worked at a field hospital in Bergamo and were based in and around the nearby city of Brescia.
But it is unclear how effective the mission was. Russia's military said its field hospital had taken in 93 patients and 62 of them had recovered and been discharged. Other personnel were filmed disinfecting buildings in the area.
Italy's La Stampa newspaper last month quoted unnamed sources as saying 80% of the Russian aid was "useless".
Concerns were also expressed that a Russian military mission had been allowed to operate within 50km (30 miles) of a US military base in a Nato member state.
According to La Repubblica newspaper, Italian armed forces set up an escort system for the Russian military personnel.
It also reported that Russia sent another full flight of supplies last week, suggesting the team were not aware their deployment was soon coming to an end.
It has officially recorded more than 10,000 new confirmed cases for the past four days in a row, and now has the sixth highest reported infection number worldwide. The reported death toll is 1,537.
President Putin told regional leaders on Wednesday to begin plans to lift lockdown restrictions, but cautioned against moving to quickly.
"The price of even the smallest mistake is the safety, lives and health of our people," he said. "We should be moving forward gradually."
In contrast, Italy has begun to lift its own lockdown measures.
People are now allowed to visit relatives in small numbers, and parks, factories and building sites have reopened. Although the number of deaths announced on Wednesday rose by 369, the highest for a week, there was a record fall of almost 7,000 current infections.
On Wednesday Russian culture minister, Olga Lyubimova, became the third member of the government diagnosed with Covid-19.
Prime Minister Mikhail Mishutin has temporarily stepped aside while he recovers. Construction minister Vladimir Yakushev said he had been diagnosed last week and went to hospital for treatment.
Mr Putin said on Wednesday the prime minister had only a mild temperature, and that the two were in daily contact.
The president's personal approval ratings have sunk to historic lows during the pandemic. A poll conducted by Levada found 59% approved of Mr Putin, compared with 69% before the outbreak began.