By Gayatri Suroyo and Eveline Danubrata

JAKARTA (Reuters) - Six years after bowing out of a bruising battle to make Indonesian tycoons pay taxes, new Finance Minister Sri Mulyani Indrawati is back to finish what she started - this time with the full backing of reformist President Joko Widodo.

Under former President Susilo Bambang Yudhoyono, Indrawati steered the Indonesian economy through the global financial crisis and gained the respect of financial markets with a drive to stamp out corruption.

But Indrawati, who was ranked number 37 on the Forbes list of the world's 100 most powerful women this year, made a formidable political opponent in tycoon-politician Aburizal Bakrie, the then-chairman of Indonesia's second-biggest political party Golkar.

Bakrie's coal firm was on a list of 100 top tax dodgers that Indrawati's tax office published in early 2010, to put pressure on the business elite to pay up.

Even before then, there was bad blood between them.

"She doesn't understand a thing about the real sector," Bakrie told Reuters in an interview in 2009. "...as a cashier she is good." (http://bit.ly/2admXdh)

Four months after naming and shaming the tax dodgers on the list, she was gone. Indrawati, who has a doctorate in economics from the University of Illinois, resigned under a barrage of criticism for allegedly causing state losses during a bank bailout. She denied any wrongdoing.

She then joined the World Bank, where she was managing director and chief operating officer, the number two post after the president.

Fast forward six years and a lot has changed. Widodo was elected to office in 2014 by voters keen to sweep out the old guard. He offered Indrawati a ministerial post when he took power, a high-ranking government official told Reuters.

She declined at the time, because Golkar was in opposition and Bakrie was still in charge of the party, the official said, declining to be named due to the sensitivity of the matter. As an opposition party it would not have shied away from criticizing a government minister.

Two years later, Bakrie is no longer Golkar chairman - he was made head of its advisory board after a bitter internal dispute - and the party has joined Widodo's coalition. This helped convince Indrawati to take the job, the official said.

When asked why she accepted Widodo's offer, Indrawati told reporters after her inauguration on Wednesday it was "a noble task", but declined to comment further.

Indrawati is the right choice as she had "good economic skills", Bakrie told Reuters on the sidelines of a Golkar meeting on Thursday, and denied there was any conflict between them.

"STRAIGHTFORWARD AND A LITTLE TOUGH"

Widodo personally asked World Bank President Jim Yong Kim for permission to bring Indrawati home as finance minister, Cabinet Secretary Pramono Anung told reporters on Wednesday.

"I know that President Widodo's highest priority is the ongoing reform program, and Sri Mulyani's return will increase confidence in Indonesia's performance and will be highly important for promoting transparency," Kim said in a letter to the World Bank staff.

Indrawati commands respect from the rank and file in the finance ministry and was received with loud applause from 700 tax officers on Thursday when she entered a state palace hall in Jakarta for a briefing by the president.

"She is straightforward and a little tough", but she looks after her staff well and nurtures team spirit, former finance minister Chatib Basri, who was once an adviser to Indrawati, told Reuters.

Widodo needs Indrawati more than ever now, as he has staked political capital on a tax amnesty scheme launched this month aimed at bringing back billions of dollars stashed overseas to rejuvenate Indonesia's sluggish economy.

Indrawati has already told the tax office to work hard to prepare for the first three months of the amnesty, when most cash is likely to be repatriated.

"Not only the tax amnesty, but the state budget itself must be credible," she said on Thursday. "The most important thing is that I want to build certainty. Certainty for the internal finance ministry and the tax office, certainty for businessmen and the economy, certainty about where the government's policy is headed because it is important to get the economy working."

Growth in Southeast Asia's biggest economy is expected to improve only slightly to 5.2 percent this year from 4.79 percent in 2015, the slowest growth rate in six years.

Nevertheless, Indrawati's decision to join what analysts say is an economic 'dream team' has been cheered by investors and is seen as a coup for Widodo.

"Sri Mulyani is a tough, clear-headed, reform-minded economist who knows her way around the complex world of Indonesian politics, and understands how Indonesia engages with the rest of the world," said Hal Hill, professor of economics at Australian National University.

"I think everybody has moved on from the painful events of 2008-2010."

(Additional reporting by Hidayat Setiaji, Agustinus Beo Da Costa and Kanupriya Kapoor; Writing by Randy Fabi; Editing by Simon Webb and Raju Gopalakrishnan)