"We should not be second-guessing. We should be supporting him," Clinton said in a telephone interview while traveling in Australia.
Clinton, who left office in January after serving two terms, said he was stunned and angered by the attacks in New York and Washington.
"The most important thing is, we all have to be strong, calm good Americans now and rally behind the president and support the actions he will doubtlessly take ... in the days ahead in both rescue and reconstruction of the area and especially in investigating and taking whatever action is necessary" against those responsible, Clinton said.
"The main thing is, we must send a clear and unambiguous message to the world that the people of America are completely 100 percent united, and we're going to follow our leaders and support whatever action [Bush] takes," he said.
Clinton had been president for only a few weeks when terrorists blew up a truck bomb in the World Trade Center's basement in February 1993, killing six people and injuring more than 1,000 others.
He also dealt with the April 1995 bombing of the Murrah Federal Building in Oklahoma City, where 168 people died. Timothy McVeigh was executed this year for the crime and conspirator Terry Nichols faces the death penalty.
On Bush and his team, Clinton said: "We're going to have to give them some time. They're going to have to work on this. ... I know they're going to work overtime. I know they're going to do a good job."
Former Vice President Al Gore, who has kept a low profile since losing the 2000 presidential election to Bush, also threw his support behind Bush.
"Like all Americans, I strongly support President Bush's statement that we will use every resource at our disposal to find out who did this and hold them accountable," Gore said in a statement.
"It is an unspeakable tragedy, and my heart goes out to the victims and their families." Clinton praised Bush for taking the advice of the Secret Service and flying from Florida to military bases in Louisiana and Nebraska since the tragedy.
"Nobody should be questioning any decisions he makes," Clinton said. "We ought to be hanging in there, giving his national security team the time it takes."