In 1999, Welch appeared in NBC's Third Watch. In 2000, he appeared in the television series Law & Order: Special Victims Unit, the short film Custody, and the television film Hamlet. He then appeared in an episode each of The Practice, Law & Order: Criminal Intent, and Whoopi.
In 2004, Welch appeared in the films Marie and Bruce, The Stepford Wives, and Keane. In 2005, he again appeared in Law & Order: Special Victims Unit, and also had roles in the films The Interpreter and War of the Worlds. In 2006, he had roles in the television shows, The Book of Daniel and The Sopranos, as well as the films The Hoax and The Good Shepherd.
Welch had roles in the 2008 films What Just Happened and Synecdoche, New York. He appeared as David Haig in the television series Law & Order from 2008–2010. In 2009, he appeared in the film Whatever Works and the television series Nurse Jackie. In 2010, he appeared as Grant Test in the AMC series Rubicon. In 2012, he appeared in the films The Master and Lincoln as Clerk of the House Edward McPherson, as well as a role in the television series Elementary. In 2013, he also had a role in the films Syrup and Admission, with a role in the television series Golden Boy.
Welch died due to complications of cancer on December 2, 2013, at a hospital in Santa Monica, California. He was 48 years old. Welch is survived by his wife, daughter, parents, and siblings.
