The southern terminus of SR 605 is at a signalized intersection with U.S. Route 62 (US 62) in the northeastern Columbus suburb of New Albany.

Its northern terminus is also at SR 37, a signalized intersection approximately 3 miles (4.8 km) southeast of Sunbury.

The route quickly leaves downtown New Albany and heads northward.

[1][3] A road from New Albany to north of Center Village first appeared on maps in 1924.

[6] By 1994, jurisdiction of the portion of SR 605 between SR 37 and the US 36/SR 3 concurrency was transferred from the Ohio Department of Transportation (ODOT) to Delaware County, who renamed the road to County Road 605.