NY 345 was assigned as part of the 1930 renumbering of state highways in New York; however, it originally followed a different alignment south of the hamlet of Madrid.

Ownership and maintenance of NY 345's original routing south of Madrid was transferred from the state to the county and the village of Canton as part of the exchange.

[4] It exits the village shortly afterward, at which point the route becomes maintained by the New York State Department of Transportation.

[3] It heads northwestward on a linear path through the town of Potsdam, passing through mostly undeveloped areas comprising open fields and forests.

[4] The highway continues into the community, where the route becomes Bridge Street and intersects NY 310 on the eastern bank of the Grasse River.