She received an overwhelming majority, 397 of the 611 valid ballots, in a vote in the Bundestag lower house of parliament, making her Germany's eighth postwar leader.
The vote came two months after her Christian Democrats (CDU) narrowly won a general election against outgoing leader Gerhard Schroeder's Social Democrats (SPD), who served for seven years in a coalition with the Greens.
"Dear Dr. Merkel, you are the first democratically elected female head of government in Germany. That sends a strong message to many women and surely some men as well," parliamentary speaker Norbert Lammert said to laughter.
Mr Schroeder, 61, was the first to shake her hand.
The 51-year-old Merkel, who is also Germany's youngest postwar leader, cracked a small smile as the results were announced and appeared to fight back tears as the deputies applauded her.
"I wish you much luck, strength and God's blessing," President Horst
Koehler said.
The conservative faces a daunting task, particularly as she has been forced to head up an unwieldy left-right "grand coalition" with her political rivals.
The razor's-edge election result underlined Germans' rejection of her more radical economic reform plans in favor of one leavened with the SPD's traditional leftist policies on the labor market and the welfare system.
"I am firmly convinced that we will together be successful in renewing and further developing our social welfare state so that it can also be a source of strength for our society and our economy in the future," SPD leader Matthias Platzeck said, congratulating Mrs Merkel.
Mrs Merkel has set a goal of returning Germany to the top three countries in Europe for economic growth within 10 years and slashing the 11 percent unemployment rate during her four-year term.
A self-effacing pastor's daughter who lacks the charisma and occasional flamboyance of her predecessor, Mrs Merkel has brushed off comparisons with Britain's Margaret Thatcher.
Indeed, the constraints of the power-sharing government, Germany's first since the 1960s, will keep her from forging a radical path akin to that of the "Iron Lady".
On foreign policy, she has pledged broad continuity in relations with key allies, but aims to mend fences with United States after ties were strained over Berlin's opposition to the Iraq war, and to avoid favoring ties with Russia over those with eastern European states.
Russian President Vladimir Putin hailed Mrs Merkel's election, saying he was committed to deeper ties between the two countries and "convinced" of the "deepening of the strategic partnership."
French President Jacques Chirac said he hoped Paris and Berlin would give "new impetus" to the crisis-wracked European Union.
"I am conscious of your desire to contribute to an even closer rapprochement of our two countries," he said in a statement.
Mrs Merkel, a trained physicist, did not begin her political career until after the Berlin Wall fell in 1989, leading many observers to brand her an "outsider" who may nevertheless be better able to transcend the often clubby world of German politics.
Mrs Merkel rocketed to the top of her party in 2000 after publicly calling for her mentor Helmut Kohl's ouster, a brazen move that made her several powerful enemies.
Mr Schroeder, who finally relented in a bitter power struggle with Mrs Merkel after the September election, gave her a gracious welcome at the chancellery as he handed over the keys in a ceremony, presenting her with a bouquet of flowers and wishing her "all the best."
"I would like to thank you for what you did for our country," Mrs Merkel told Mr Schroeder, citing in particular his controversial economic reform drive Agenda 2010.
"You can be sure I will continue in a responsible manner with what you accomplished here as German chancellor."
Mrs Merkel will embark Wednesday on a trip to Paris and then meet with EU leaders in Brussels, followed by a visit to London Thursday, in three brief get-acquainted visits with Germany's closest European allies.
Mr Schroeder, for his part, plans to retire from parliament Wednesday and has said he wants to return to practicing law.