Menem was originally slated to take office on December 10. However, amid a massive economic downturn, Alfonsin opted to transfer power to Menem five months early, on July 8. Menem's accession marked the first time since Hipólito Yrigoyen took office in 1916 that an incumbent government peacefully surrendered power to a member of the opposition.

Menem assumed duties in the midst of a major economic crisis which included hyperinflation and recession. After a failed stabilization program sponsored by Bunge y Born (a leading agribusiness firm), and another one involving the conversion of time deposits into government bonds, newly appointed Finance Minister Domingo Cavallo introduced a series of reforms in 1991 and pegged the value of the Argentine peso to the U.S. dollar. This Convertibility Plan was followed by a wholesale privatization of utilities (including the oil company Yacimientos Petrolíferos Fiscales (YPF), the post office, telephone, gas, electricity and water utilities). A massive influx of foreign direct investment funds helped tame inflation (from 5,000% a year in 1989 to single digits by 1993) and improved long - stagnant productivity, though at the cost of considerable unemployment.

Menem's successful turnaround of the economy made the country one of the top performers of the developing countries in the world. Argentina's GDP (below 1973 levels when Menem took office) increased 35% from 1990 to 1994 and fixed investment, by 150%. Negotiations with Brazil resulted in the Mercosur customs union, in March 1991, and on November 14, he addressed a joint session of the U.S. Congress, being one of only three Argentine presidents who had that distinction (together with Raúl Alfonsín and Arturo Frondizi). Menem was reelected to the presidency by a large majority in the 1995 elections.

The early success of the dollar peg (when the dollar was falling) was followed by increasing economic difficulties when the dollar began to rise from 1995 onwards in international markets. High external debt also caused increasing problems as financial crises affecting other countries (the Tequila Crisis in Mexico, the East Asian financial crisis, the Russian financial crisis in 1998) led to higher interest rates for Argentina as well. At the end of his term, Argentina's country risk premium was a low 6.10 percentage points above yield on comparable U.S. Treasuries.

Some years after the end of Menem's term, the combination of fixed rate convertibility and high fiscal deficits proved unsustainable, despite massive loan support from the International Monetary Fund, and had to be abandoned in 2002, with disastrous effects on the Argentine economy. Though most of the State enterprises privatized during his tenure remain in private hands, perhaps the most significant economic legacy of his administration, private pension funds, have since largely been returned to the public sector. First licensed in 1994, these grew to over US$ 30 billion in assets, but suffered large losses during the 1998 - 2002 crisis, and by 2008, depended on subsidies to cover minimum monthly pensions. Most affiliates, moreover, had stopped making contributions. The 2008 financial crisis exacerbated the problem, and the funds were largely replaced by the public social security system in late 2008.

Menem's presidency was initially bolstered by the significant economic recovery in evidence following Cavallo's appointment as Economy Minister, and his Justicialist Party enjoyed victories in mid term elections in 1991 and 1993, as well as in his 1995 campaign for reelection. Menem's government re-established relations with the United Kingdom, suspended since the Falklands War, within months of taking office. He also earned plaudits for resolving territorial disputes with neighboring Chile, and during his administration, over 20 border issues with Chile - including the arbitration of the especially serious Laguna del Desierto dispute - were peacefully solved.

In 1994, after a political agreement (the Olivos Pact) with the Radical Civic Union party leader, former president Raúl Alfonsín, Menem succeeded in having the Constitution modified to allow presidential re-election, so that he could run for office once again in 1995. The new Constitution, however, introduced decisive checks and balances to presidential power. It made the Mayor of Buenos Aires an elective position (previously the office belonged to a presidential appointee and was in control of a huge budget), to be lost to the opposition in 1996; the president of the Central Bank and the Director of the AFIP (Federal Tax & Customs Central Agency) could only be removed with the Congress's approval. It also created the ombudsman position, as well as a board to propose new judicial candidates.

His tenure suffered, however, from local economic fallout due to the Mexican peso crisis of 1995, and became tainted with repeated accusations of corruption. His handling of the investigations of the 1992 Israeli Embassy bombing and the 1994 bombing of the AMIA Jewish community center was often criticised as being dishonest and superficial. He is suspected of diverting the investigation from the "Iranian clue", which would lead to the responsibility of that country in the attack.

One of the most criticized measures of his administration was the pardon he granted on December 29, 1990, to Jorge Videla, Emilio Massera, Leopoldo Galtieri and other leaders of the 1976 – 83 dictatorship convicted in the 1985 Trial of the Juntas, and some guerrilla leaders as well, on the grounds of "national reconciliation". This action sparked a protest of nearly 50,000 people in Buenos Aires. Former President Raúl Alfonsín called it "the saddest day in Argentine history." His neoliberal policies were also criticized by the left of the Argentine political spectrum and by some in the Catholic Church, and gave rise to the Piquetero movement of unemployed workers. These mounting problems and a rise in crime rates helped lead to the president's first electoral defeat, during the 1997 mid term elections.

With regards to the military, Menem ordered the forceful repression of a politically motivated uprising by a far-right figure, Col. Mohamed Alí Seineldín, on December 3, 1990, and thus ended the military's involvement in the country's political life. Menem also effected drastic cuts to the military budget, and appointed Lt. Gen. Martín Balza as the Army's General Chief of Staff (head of the military hierarchy); Balza, a man of strong democratic convictions and a vocal critic of the Falklands War, had stood up for the legitimate government in every attempted coup d'état throughout his senior career, and gave the first institutional self - criticism about the Armed Forces' involvement in the 1976 coup and the ensuing reign of terror. Following the brutal death of a conscript, Menem abolished conscription in 1994, decisively ending a military prerogative over society and its self - perceived role as an institution that it "made men out of boys".

Menem's attempt to run for a third term in 1999 was unsuccessful, as it was ruled to be unconstitutional. Opposition candidate Fernando de la Rúa defeated Eduardo Duhalde, the nominee of Menem's party, and succeeded Menem as President.

Menem tried again four years later, winning the greatest number of votes, 24%, in the first round of the April 27, 2003 presidential election. This was far from the 45% required for election (or 40% if the margin of victory is 10 or more percentage points), and so a second round run-off vote between Menem and second place finisher and fellow Peronist Néstor Kirchner, who had gotten 22%, was scheduled for May 18. However, by this time Menem had become very unpopular, and the consensus of most polls was that he faced almost certain defeat by Kirchner in the runoff. A few polls showed Menem losing by 40 points. Certain that he was about to face a humiliating electoral defeat, Menem withdrew his candidacy on May 14, effectively handing the presidency to Kirchner.

In June 2004 Menem announced that he had founded a new faction within the Justicialist Party, called "People's Peronism," and stated his ambition to run in the 2007 election.

In 2005, the press reported that he was trying to make an alliance with his former Minister of Economy Domingo Cavallo to fight in the parliamentary elections. The alliance was apparently frustrated; Menem said that there had been only preliminary conversations. In the 23 October elections, Menem won the minority seat in the Senate representing his province of birth. This was viewed as a catastrophic defeat, signaling the end of his political dominance in La Rioja, since the two senators for the majority were won by President Kirchner's faction, locally led by former Menemist governor Ángel Maza. It was the first time in 30 years that Menem lost an election.

Menem ran for Governor of La Rioja in August 2007, but was defeated, receiving third place with about 22% of the vote. Following this defeat in his home province, he withdrew his candidacy for president. At the end of 2009 he announced that he intends to run for the presidency again in the 2011 elections.

On June 7, 2001, Menem was arrested over an arms export scandal relating to exports to Ecuador and Croatia in 1991 and 1996, and remained under house arrest until November. He appeared before a judge in late August 2002 and denied all charges. It was hinted that Menem held more than USD $10 million in Swiss bank accounts. However, the Swiss banks and authorities denied these allegations.

Menem and his second wife Cecilia Bolocco, who had had a child since their marriage in 2001, moved to Chile. Argentine judicial authorities repeatedly requested Menem's extradition to face embezzlement charges, but this was rejected by the Chilean Supreme Court, as under Chilean law people cannot be extradited for questioning. On December 22, 2004, he returned to Argentina after his arrest warrants were cancelled. He still faces charges of embezzlement and failing to declare illegal funds outside of Argentina. In August 2008, it was announced Menem was under investigation for his role in the 1995 Río Tercero explosion, which is alleged to have been part of the arms scandal involving Croatia and Ecuador. In December 2008, the German multinational Siemens agreed to pay an $800 million fine to the United States government, and approximately €700 million to the German government, to settle allegations of bribery. The settlement revealed that Menem received about US$2 million in bribes from Siemens in exchange for awarding the national ID card and passport production contract to Siemens; Menem denied the charges.