According to one version, the name of the village is connected to the name "Nestor," which in Ukraine sounded like "Neshchir." In 1794, landowner Ivan Pavlovich Gudim-Levkovich built a stone church of the Transfiguration of the Lord in Neshcherov with side chapels in honor of Saint Paul the Confessor, the holy equal-to-the-apostles first martyr Thecla, and the Beheading of the head of Saint John the Baptist.

The Gudim-Levkovich family was known for its members who held important positions in the administration of Kyiv from the 17th to the 19th centuries. The founder of the family, Peter Levkovich, known as Gudima, was from Serbia and held the position of Kyiv's burgomaster in the second half of the 17th century. In 1692, he built a stone church of Saint Elijah the Prophet in Kyiv on Podil at the site of an ancient Rus church mentioned in the chronicles in the year 944. His son, merchant Ivan Gudima, made a significant contribution to the construction of the Greek church of Saint Catherine the Great Martyr in Kyiv in 1739. Ivan's son, Kyiv hundredman Pavel Gudima, erected a chapel of the Beheading of the head of Saint John the Baptist next to the church of Saint Elijah the Prophet and a separate bell tower. His brothers Vasily and Joseph were also Kyiv burgomasters, while Feodor served as a priest in the Holy Elijah Church. Pavel's son, Ivan Gudim-Levkovich, was a Kyiv hundredman from 1772, and after the abolition of the hundred in 1782, he became the leader of the nobility of Kyiv County. He was buried near the Transfiguration Church he built in the village of Neshcherov. One of his descendants became a well-known Kyiv financier, while another became a civil governor.

During the Soviet era, the Transfiguration Church fell into disrepair, but in the 1990s, its revival began. In 2004, a country skete of the Kyiv Holy Trinity Ioniński Monastery was established at the Transfiguration Church, and in 2005, an independent monastery was founded. Thanks to the efforts of both monasteries and the support of patrons, the restoration of the church was carried out at a high level. In addition to the main altar, a second altar was restored in honor of the Beheading of the head of Saint John the Baptist; in 2013, a chapel of the holy new martyrs and confessors of Russia was arranged in the former basement.