Born in La Porte, IN on July 14, 1844. Welch crossed the plains with his family in a prairie schooner at age thirteen and settled on a farm near Portland, OR. After graduating from nearby McMinnville College, he accepted a position in Portland at Walling's Printing Office. Coming to California in 1866, he lived for a brief period with his aunt in Dixon before moving to San Francisco. While employed as a typesetter with the Call and Bulletin, Welch studied art with Virgil Williams and was an apprentice in the studio of J. W. Ogilvy in exchange for art lessons. While there, he made the acquaintance of a wealthy patroness who financed a four-year scholarship for further study in Europe. In 1874 he sailed for Munich where he entered the Royal Academy under Dietz, Piloty, and Leibl. While in Munich he became close friends with Frank Duveneck (who painted his portrait), Wm M. Chase, and John Twachtman. Leaving Germany, he spent nearly four years in Paris where he continued studying while living on a houseboat on the Seine. Welch returned to the U.S. in 1881 and painted for a while in the Hudson River area where he met Ludmilla Pilat whom he married in 1883. He worked for lithographer Louis Prang in Boston, and followed portrait and cyclorama commissions to Philadelphia, Chicago and Australia. Upon returning from Australia in 1889, he was active in San Francisco for a while before returning to New York for Ludmilla. After spending several months at the World's Fair in Chicago in 1893, the couple returned to California. After one year in Pasadena, they moved north to the San Francisco Bay area. Poverty stricken but deeply in love, they camped out in the hills of Marin County until a suitable cottage could be found in nearby San Geronimo Valley. There the Welches began painting the poetic scenes of rural Marin that were to bring success and freedom from financial worry. Due to Thad's health they were forced to seek a milder climate and in 1905 moved to Santa Barbara where he remained until his death on Dec. 19, 1919. Member: Bohemian Club; San Francisco Art Association. Exh: Munich Academy, 1876 (bronze medal); Paris Salon, 1880, Calif. State Fair, 1895, 1902. In: Oakland Museum; CHS; San Diego Museum; Frye Museum (Seattle).

A painter of landscapes, portraits, and genre, he depicted wide-ranging subjects in Europe and the United States but is best known for his views of Marin County, California.

As a young child, he crossed the plains with his family and settled in Oregon before moving to California. There, as a teenager, he studied art at the California School of Design in San Francisco and impressed a local patron so much that from him, he earned a scholarship to Munich, Germany in the 1860s. He remained in Europe for several years, becoming close friends and painting companions with Frank Duveneck and William Merritt Chase.

During the 1880s and early '90s, he roamed the United States working on various art projects and in 1889, he visited Santa Fe,k New Mexico where he painted colorful views of the adobes as well as Native American portraits. One of his best friends during this time was John Twachtman, American Impressionist. He did several architectural scenes of the World's Columbian Exposition in Chicago in 1893. Shortly after, he moved to the Los Angeles area and in 1897, he visited Oregon and painted a panoramic townscape of Portland.

Towards the end of the 19th century, he settled in Marin County, California, and in 1904, he and his artist wife, Ludmilla, spent a season painting in Yosemite National Park.

As a young child, Welch crossed the plains in a covered wagon and settled in Oregon where he lived until he moved to California in the 1860s. His talent for art won him a scholarship to Munich in the 1870s and he remained abroad for several years, befriending Frank Duveneck and William Merritt Chase among others. During the decade of the 1880s and part of the '90s Welch roamed the country working on various art projects.

He settled down in Marin County towards the end of the century. He received his first real measure of prosperity painting the rolling hills of Marin in a more realistic style than his earlier Munich-inspired works. By 1906 he was esteemed as a painter of "distant hills in sunlight, rich and warm foreground with cattle, trees and grasses" to quote Will Sparks writing in the San Francisco Call (September 2, 1906). The great charm of Welch's Marin paintings spawned a tradition of beautiful hillside landscapes that was carried well into the 20th century by such artists as Jack Wisby and Louis Rea. In 1905 he moved to Santa Barbara where the warmer climate restored his failing health. He continued to paint Marin County scenes-as well as the hills near his studio in Santa Barbara-until his death in 1919.