Born in Clarion County, Pennsylvania, Corbett graduated from Washington and Jefferson College (Washington, Pennsylvania) and from Princeton Theological Seminary. With his wife, Lizzie (Culbertson), he sailed for China in 1863, and after a six-month voyage around the Cape of Good Hope and shipwreck off the China coast, they finally arrived at Yantai (Chefoo) in the middle of winter, 1865. After several years in Dengzhow (P'eng-lai, or Tengchow), they established a permanent residence at Yantai and began evangelistic work. Along with colleagues Calvin Mateer and John Neius, Corbett developed the methodology that would plant the gospel in the soil of northern China and make Shandong the strongest Presbyterian mission in China. Wide itineration throughout the countryside, rather than concentrated efforts in the cities, was the main feature of the Shandong plan. Corbett was described as an "indefatigable itinerator," and he traveled over the whole province by horse, mule cart, and foot. Added to his travel difficulties were incidents in which he was reviled and stoned.
Corbett believed in using unconventional methods. He rented a theater and converted the back rooms into a museum stocked with objects of interest from around the world. After a service, the museum doors would be opened. In 1900, 72,000 people listened to his preaching and visited the museum. A crowning achievement was the organization and development of Shandong Presbytery. By the year of Corbett's death, there were 343 organized churches and chapels throughout the province, with more than 15,000 communicant members. In 1906 he was elected moderator of the General Assembly of the Presbyterian Church, U.S.A. Altogether, Corbett ministered in China for 56 years.