The Republican-dominated Senate earlier confirmed conservative judge Alito by a near party-line 58 to 42 vote.
Judge Alito, 55, a federal appeals court judge, has taken the seat vacated by departing justice Sandra Day O'Connor, who was the first woman ever seated on the court.
Mr Alito took the oath in a brief ceremony at the Supreme Court.
A White House ceremony in Alito's honour will take place on Wednesday, at which he is to take his oath a second time.
Mr Bush on Tuesday said he was "pleased" by the Senate's endorsement of Mr Alito, whom he described as a "brilliant and fair-minded judge."
"He is a man of deep character and integrity, and he will make all
Americans proud as a justice on our highest court," Mr Bush said.
Although he cleared his confirmation vote by a comfortable margin, Mr Alito garnered fewer votes than any Supreme Court justice since Clarence Thomas, a polarizing nominee who is perhaps the court's most conservative justice, was confirmed in 1991.
Despite the lack of bipartisan support for Mr Alito, Senate Majority Leader Bill Frist hailed the confirmation as a major triumph for Mr Bush.
"To President Bush, I say, thank you for nominating such an exceptionally qualified individual as Sam Alito to serve on the Supreme Court," Mr Frist said moments before the final tally.
"To Judge Alito, I say, you deserve a seat on the Supreme Court. Today, you will become the 110th justice to serve on the Court throughout America's history. It is a seat that is reserved for few, but that impacts millions," Mr Frist said.
In September, the Senate approved Bush nominee John Roberts to be chief justice. In contrast to Mr Alito, half of the Senate's Democrats voted to approve Mr Roberts, whom they viewed as conservative but not extreme. He was confirmed by a vote of 78-22.
Defeated Democrats said the confirmation was a major blow that will likely yield decades of decidedly conservative high court rulings, now that the president has succeeded in installing two staunchly right-of-centre justices to the court in a matter of a few months.
"Millions of Americans will come to know that the lasting legacy of this day will be ever more power for the president and ever less autonomy for the individual," Democratic Senator Charles Schumer predicted on the Senate floor on Tuesday.
Mr Schumer accused Mr Bush of "packing the court with yet another reliable extreme voice," and called Mr Alito's views "well out of the mainstream".
Only one of the Senate's 55 Republicans, moderate Lincoln Chafee, broke ranks with his party to vote against Mr Alito, while four Democrats defected to vote with Republicans.