Bush said Friday that Barney, who was 12, suffered from lymphoma, The Washington Post reported.
"Barney was by my side during our eight years in the White House," Bush wrote in a statement. "He never discussed politics and was always a faithful friend. Laura and I will miss our pal."
Former New Jersey Gov. Christine Todd Whitman, who served as head of the Environmental Protection Agency in the early years of the Bush administration, gave the couple the dog in 2000 as a birthday present for Laura Bush.
Bush, who has been learning to paint since his return to Texas, released a portrait of Barney, The Dallas Morning News reported.
Barney became something of an Internet celebrity in Washington. He had a Barney Cam recording his activities and a website, Barney.gov.
"Barney guarded the South Lawn entrance of the White House as if he were a Secret Service agent," Bush said in the memorial statement. "He wandered the halls of the West Wing looking for treats from his many friends. He starred in Barney Cam and gave the American people Christmas tours of the White House. Barney greeted Queens, Heads of State, and Prime Ministers. He was always polite and never jumped in their laps."
Barney is survived by Miss Beazley, a Scottish terrier Bush gave his wife in 2005.