"It would be such an honor to work for the people of Tennessee," Gore said in a statement Sunday. "However, I have decided that it is not right for me, right now, to seek to represent them in the United States Senate."
Rep. Bob Clement will run for the Senate.
Gore, wife of former Vice President Al Gore, spent the weekend discussing the Senate race with associates. She had cut short a trip to California to return to Tennessee on Saturday to consider the race.
Word first emerged Thursday that Tipper Gore, who has never sought elective office, was considering running for the open seat. Democratic sources said she had to make a decision quickly because Clement wants to run.
Byron Trauger, a friend of the Gore family, said, "There was a developing consensus in Tennessee for Bob before she was interested."
Trauger said Gore "very seriously" considered running. In the end, he said, "She put aside whatever her own interests were in the Senate in favor of consensus."
Clement said he was grateful for Gore's commitment to public service.
"She has fought courageously for issues that are near and dear to her heart," he said in a statement. "No matter what role she chooses for the future, I am sure she will continue to fight for those issues and for Tennessee in the years ahead."
Al Gore held the Tennessee seat from 1985 to 1993. When he was elected vice president as Bill Clinton's running mate, Democrat Harlan Mathews was appointed temporarily to replace him. In 1994, Republican Fred Thompson defeated Democratic Rep. Jim Cooper to replace Mathews.
The Senate seat opened up when Thompson announced March 8 that he would not seek re-election this November. The surprise decision turned what had been considered a safe Republican seat into one expected to be among the most highly contested this fall.
The filing deadline for the race is April 4.
On the Republican side, former Tennessee Gov. Lamar Alexander and Rep. Ed Bryant are running.
Gore, 53, is known for her advocacy on mental health issues. She became interested partly because her mother suffered from depression. She also has acknowledged being treated for depression after her son, Albert III, then 6, was hit by a car in 1989 and almost died.
"I am passionate about mental health and family issues and my work in those areas will continue to be my focus," she said in her statement Sunday. "I will also work to elect the Democratic nominee for the United States Senate and all our Democratic candidates."