The Senate on Tuesday voted 58-42 to confirm Alito - a former federal appellate judge, US attorney, and conservative lawyer for the Reagan administration from New Jersey - as the replacement for retiring Justice Sandra Day O'Connor, who has been a moderate swing vote on the court.
Alito is expected to align himself with the court's solidly conservative bloc and could affect the outcome of votes on key social issues such as abortion and civil rights.
Alito watched the Senate vote from the White House and was to be sworn in at the Supreme Court later in the day.
He was expected to attend Bush's State of the Union address to Congress on Tuesday night with fellow justices.
O'Connor's seat has long been viewed as pivotal since for years she has been the swing vote in a series of 5-4 decisions on social issues. Roberts replaced a fellow conservative, the late William Rehnquist, so he did not change the balance on the court.
Democratic critics had voiced fear that Alito would embrace an ideological agenda, but backers noted that he promised to administer justice for all and received the American Bar Association's top rating.
Though he opposed abortion while serving in the Reagan administration two decades ago, Alito promised at his confirmation hearing to respect legal precedent, which includes a 1973 Supreme Court decision that legalised abortion.
Still, to the consternation of foes, he did not say how he would rule.
Alito, 50, and Roberts, 51, appear certain to help shape the American way of life for years as key figures in the legacy of the 43rd president.
Bush won two terms as president vowing to put staunch conservatives on the Supreme Court, the nation's final legal arbiter.