PITTSBURGH—Royal Dutch Shell PLC gave the long-awaited go-ahead to a multibillion-dollar petrochemical plant that is expected to give a lift to Pennsylvania and the struggling shale-gas industry.

The company first announced in 2012 that it was considering building a plant about 30 miles north of Pittsburgh in a faded industrial area along the Ohio River once lined with steel mills. The plant is expected to create 6,000 construction jobs and 600 permanent jobs and draw chemical companies and other manufacturers to the region.

...