Residents had a four-hour window to leave before a convoy of 25 buses, with space for 750 people, left the town on Friday afternoon - along with ambulances for people with limited mobility.
However, some in Ukraine recoiled at the sight of him standing beside a representative of the Russian occupying power, which has killed many of the city's residents and made life unbearable for the rest.
The impact of years caught between the frontlines was visible on the weary faces of the residents, with some hobbling on crutches, others needing wheelchairs, and elderly residents so weak they were carried on stretchers.
Families cried as they embraced relatives they had not seen for years, capturing the sheer relief of three years of desperate worry and fear that they would never see each other again.
Several hundred people are understood to have decided to stay in the war-torn city despite widespread devastation and the lack of gas, electricity, and running water.
Conditions had become desperate in the city, where escape was highly dangerous because routes out were mined and subject to drone attack.
Residents had been trapped without food, water, and electricity, and many resorted to cooking garden weeds to survive.
Ukrainian military positions lie just 5km (3.1 miles) from Oleshky.
Russia said on Thursday that it had prepared"dozens of tonnes"of aid for the residents who do not wish to leave, including food, medicine, hygiene products and fuel for generators.