Synivka was first mentioned in 1669. According to local legend, its name derives from the phrase "Land of the Sons of Veletskyi" (Ukrainian: Земля синів Велецького, romanized:Zemlia syniv Veletskoho), after a noble family which had been given ownership of the village by Hetman of the Zaporizhian HostIvan Skoropadsky.[2]
Synivka was taken over by the Russian Soviet Federative Socialist Republic in January 1918, and a kolkhoz named after Vladimir Lenin was established in the village afterwards. During World War II two partisan groups were established, including a group of Komsomol members led by M. Artiukh, which was responsible for killing 20 German soldiers and officers. A total of 165 residents were killed during the war.[3]
Prior to the 2020 administrative division reform in Ukraine, Synivka was part of Lypova Dolyna Raion.[3]
A series of protests occurred in the village in 2020, in opposition to the plowing of fields. The protesters cited livestock grazing as a reason for their opposition to the plowing.[4]