Moussa, who became popular with ordinary Egyptians as head of the Cairo-based League, is tipped as a front-runner in next month's election.
Many Egyptians fondly remember how he regularly slammed Israeli policies and in 2003 warned against the US-led invasion of Iraq, saying it would "open the gates of hell."
In 2001, around the time he resigned from his post as Egypt's foreign minister to take up the League job - amid speculation he was pushed by a president who felt Moussa was overshadowing him -- an Egyptian artist wrote a song that caught on with the lyrics: "I hate Israel ... I love Amr Moussa".
Yet however popular he remains, the biggest challenge for the man who describes himself as a liberal nationalist may be to convince Egyptians that he can bring change and that he is not part of the old, discredited order.
"The question is not old guard or new guard. The question is either you were part of the corrupt people that have done a lot of harm to the country or among the people who have worked and done their duty according to the highest standard they could do," Moussa told Reuters last year early in campaigning.
Moussa has since toured the length and breadth of the country, waging one of the longest campaigns among any of the 13 presidential candidates now battling in an historic election race that begins with a first round vote on May 23-24.
He possesses a detailed, 80-page program outlining steps to eradicate illiteracy and drive growth. For the first 100 days, his plan includes scrapping a hated state of emergency that was in place throughout Mubarak's three decades in power, restoring order and injecting cash to kick start the economy.
Moussa also pledges to form a national security council, which would include among its members top military officers, a step that could reassure the army which is likely to be wary of dealing with any president who for the first time in six decades has not been drawn from their ranks.
Yet he insists the generals who have ruled since Mubarak was deposed last year will no longer be in charge after they formally hand power to the next president by July 1, even though analysts expect the military to retain broad influence for years from behind the scenes.
"The president will be the boss," he told reporters in April, although he added that discussion about the relationship between the president and the military was not a priority when Egypt faced a political and economic crisis.Disdain
Abroad, Moussa is a well-known figure on the world stage and could prove a reassuring presence for Western nations wary of the rise of Islamists in the Arab world's most populous state.
But Israel, long a target for his criticism, may not welcome having him in charge. A writer in Israel's Haaretz newspaper described Moussa as having intense "disdain" for Israel.
Moussa like other candidates says he would uphold Egypt's 1979 peace treaty with Israel, despite criticism of the Israeli government.
In the latest poll published by the state-owned Al-Ahram newspaper, Moussa was seen as the front-runner. He probably has the best name recognition of any candidate. But his support level has dipped from a few months ago as the race has widened.
His main rivals include Abdel Moneim Abol Fotouh, an Islamist polling second behind Moussa and who has backers ranging from liberals to hardline Islamists. He is also facing Mohamed Mursi, the Muslim Brotherhood's candidate.
Both have railed against candidates in the race from the 'feloul', an Arabic term meaning 'remnants' of the old order, referring to officials who served under Mubarak.
Moussa, in turn, when asked about his Islamist rivals, said Egyptians "should not get into an experiment that has not been tried before". Yet, if he wins, he will have to work closely with Islamists who already dominate parliament.
His other main rival is Ahmed Shafiq, Mubarak's last prime minister and a former air force commander. Shafiq may get some support from voters wary of Islamists. He may also deflect criticism away from those linked to the old order as Shafiq held a more senior position than Moussa under Mubarak.
A new constitution is unlikely to be ready in time to offer the next leader a clear job description, but Moussa says as president he will need to be a "master lobbyist," a skill ignored during years of autocratic rule.
He has said he wants a presidential system, putting him in conflict with Islamists who favor a mixed set-up that gives both parliament and president powers. But he also said he would not oppose a French-style arrangement, where the president leads on foreign affairs and parliament has a bigger domestic role.
Asked when speaking to reporters this month if he would be willing to serve as a vice-president if he lost the race, he smiled and said: "I am very bad at being second."
CAIRO (Reuters) -- The 75-year-old former head of the Arab League has vowed to serve just one four-year term if elected Egypt's president, but Amr Moussa's Islamist rivals, who see him as a relic from Hosni Mubarak's era, say he doesn't even deserve that long.