Mr. Reagan, champion of smaller government and lower taxes, died at his home in California at the age of 93.
His wife, Nancy, and family members had gathered at his bedside at his house in the Bel Air district of Los Angeles.
President Bush, who was in Europe in part to commemorate the 60th anniversary of D-Day on Sunday, called Reagan's death "a sad hour in the life of America," the Associated Press reported. The U.S. flag at the White House was lowered to half-staff.
Mr. Reagan's body reportedly will be flown to Washington to lie in state in the Capitol Rotunda before a funeral service at the National Cathedral. His body will then be returned to California for burial at his library.
The 40th president told the world in November 1994, five years after leaving office, that he had been diagnosed with the early stages of Alzheimer's, an incurable illness that destroys brain cells.
The film star-turned-politician served as president from 1981 to 1989, becoming the first right-wing president in 50 years. His populist brand of conservative politics still inspires the Republican Party.
Much of his presidency was dedicated to winning the Cold War, and he tripled the national debt to $3 trillion as he set his sights on the demise of the Soviet Union and Eastern European communism.
Former British Prime Minister Margaret Thatcher said Saturday, "Ronald Reagan has a higher claim than any other leader to have won the Cold War for liberty and he did it without a shot being fired."
In his second term, Mr. Reagan was thrust into controversy with the disclosure that the United States had sold arms to Iran in 1985-86 and diverted proceeds to aid Contra guerillas fighting the leftist government of Nicaragua. Witnesses at congressional hearings in 1987 said he was never told of the Contra funds.
Despite the investigations, he left office in 1989 with the highest popularity rating of any retiring president in modern history. Leaving office just two weeks shy of his 78th birthday, he also was the oldest president.
His physical resilience in office was demonstrated with his survival of an attempted assassination in 1981, a 1985 colon cancer operation and 1987 prostate and skin-cancer surgery, Reuters reported.
When he was diagnosed with Alzheimer's in 1994, he wrote a letter to the nation, saying, "When the Lord calls me home ... I will leave with the greatest of love for this country of ours and eternal optimism for its future."
Mr. Reagan "leaves behind a nation he helped restore and a world he helped save," President Bush said at the U.S. ambassador's residence in Paris.
Mr. Reagan's oldest daughter, Maureen, from his first marriage, died in August 2001 at age 60 from cancer. His three surviving children are Michael, also from his first marriage, and Patti Davis and Ron from his second.