The first inhabitants of the area currently known as Greenwood were the Delaware Indians (Lenape). In 1818, the Treaty of St. Mary’s opened central Indiana to European American settlement, and by 1823 the first cabin in northern Johnson County was erected by settlers John B. and Isaac Smock on land now occupied by Greenwood Park Mall. Greenwood was first known as “Smocktown” or “Smock’s Settlement” in honor of the Smock brothers, and became “Greenfield” in 1825. Since this clashed with another Greenfield located in Hancock County, the name of the settlement was changed to “Greenwood”. Some claim the town’s name was in honor of Samuel Greenwood, who platted the community in 1872. The Polk Canning Company was essential to Greenwood’s early growth. The cannery was a major employer and canned a variety of vegetables grown in Indiana. Later, the company expanded into the dairy market and provided milk delivery to customers. At one point the cannery was the largest canning operation west of Baltimore. The cannery was eventually purchased by the Stokely-Van Camp company and retained operations in Greenwood until the 1950s. Portions of the cannery are still standing on Main Street and have been repurposed for professional office space.

Greenwood was an early and key cog in the Electric Indianapolis Interurban Railway System. In 1895, Henry L. Smith proposed and organized the Indianapolis, Greenwood & Franklin Company and graded the line to Greenwood. The Indianapolis, Greenwood & Franklin Railway was opened between Indianapolis and Greenwood on January 1, 1900 and, according to Indianapolis historian Jacob Piatt Dunn, was the Hoosier capital’s first real interurban electric railway. The railway followed what is now Madison Avenue. Greenwood was incorporated as a town under Indiana law in 1864 and became a fifth-class city in 1960. In 2010, the Greenwood City Council approved a measure to change the official status of Greenwood to second class city in accordance with Indiana Code Title 36, Article 4, Chapter 1. Greenwood is in northern Johnson County and occupies the northern half of Pleasant Township and the northeast portion of White River Township. It is bordered to the southwest by Bargersville, to the south by Whiteland and New Whiteland, and to the north, in Marion County, by the city of Indianapolis. Greenwood is 11 miles (18 km) south of downtown Indianapolis and 12 miles (19 km) north of Franklin, the Johnson county seat.

There are no navigable bodies of water within city limits. Several creeks run through the area and influence local drainage patterns, topography, and storm water management systems. Pleasant Run Creek flows from east to west across the northern half of the city, leading 5 miles (8 km) to the White River. Several municipal parks occupy the lowlands next to the creek. Grassy Creek and Tracy Ditch flow south from the city, connecting Greenwood to the towns of New Whiteland, Whiteland, and Franklin. Honey Creek originates in the southwest section of the city and after flowing through White River Township eventually joins the White River near the intersection of Smith Valley Road and Highway 37.

Greenwood is home to the U.S. headquarters of Endress+Hauser, a Swiss company that specializes in process automation and instrumentation products. The city is also home to Indiana American Water, a publicly traded utility that serves about 1.2 million Hoosiers in 126 communities. Other major employers in Greenwood include the corporate headquarters for machine tools manufacturer Nachi America and metal fabrication firm Poynter Sheet Metal. Greenwood is also home to distribution centers for Ulta, ALDI, United Natural Foods, and Nestle Waters North America; and a medical services complex for Ortho Indy. Three craft breweries are located within Greenwood. Oaken Barrel Brewing Co. has called Greenwood home since its opening in 1994. Oaken Barrel is the second oldest brewpub in Indiana. Planetary Brewing established a production center and tasting room for Greenwood customers in 2013. The city is also home to Mashcraft Brewing Company. Mashcraft operates a taproom on State Road 135.