In the summer of 1968 he won a scholarship to the Kent State University Blossom Art Program and studied under Op-Artist Richard Anuszkiewicz.
In the fall of that year, Welch had his first solo show of minimalist paintings at the Western College Art Museum in Oxford, Ohio.
At the same time, he studied the Earthworks and Non-Sites of Robert Smithson and was also influenced by a personal meeting with conceptual artist Douglas Huebler.
In 1969, Welch began graduate studies at the School of the Art Institute of Chicago in the sculpture department headed by James Zanzi.
Among his friends and colleagues at this time were Bill Beckley, Les Levine, Gordon Matta-Clark, William Wegman, and Hannah Wilke.
During his 1973 solo exhibition at the John Gibson Gallery in New York, Welch produced a series of maps drawn from the childhood memories of four elderly people.
On consecutive Saturday afternoons over the course of the exhibition, Welch engaged in a dialogue with each person about her or his hometown while he created drawings and a map from their verbal recollections.
The Memory Maps attracted the attention of social psychologists such as Stanley Milgram with whom Welch collaborated in a 1975 exhibition at the Piltzer Gallery in Paris.
In 1985, Welch was invited to participate in the Construction in Process II exhibition in Munich and created the video The Voice of Clint Eastwood in Germany.
The History of Design is a 48 ft. wide Parthenon-like pediment framing life-size photo images of young workers in the process of constructing a wall.
Beginning in 2003, Welch produced a series of sculptures, watercolors such as Yankee Stadium in Meteor Crater, and videos juxtaposing landscapes or combining geologic formations with contemporary man-made structures.
For the exhibition Domicile in 2006, French art critic Pierre Tillet wrote: Welch deals with the visual and emotional closeness of distant spaces.