* Former Swedish prime minister elected chairman
* Vows to "clean the house" after money-laundering scandal
* Analyst says market has priced in $5 bln of U.S. fines (Adds quotes, details)
By Johan Ahlander and Esha Vaish
STOCKHOLM, June 19 (Reuters) - Swedbank shareholders elected Goran Persson as chairman on Wednesday, with the former Swedish Prime Minister pledging to "clean the house" after a money-laundering scandal.
Sweden's oldest retail bank has lost its chief executive, chairman and a third of its stock market value this year as its Estonian business was embroiled in a money laundering scandal.
Swedbank, which is under investigation in the United States, the Baltics and Sweden, now faces the potential threat of hefty sanctions and fines as it seeks to regain public confidence.
The most recent allegations against Swedbank, reported by Swedish state TV in March, say it processed gross transactions of up to 20 billion euros ($22 billion) a year from high-risk, mostly Russian non-residents, through Estonia from 2010 to 2016.
Swedbank suspended its two top Estonian executives on Tuesday as part of an internal inquiry into its compliance with anti-money laundering rules which it launched in April under shareholder pressure for greater transparency.
While Danske Bank - also embroiled in a money laundering scandal - got thrown out of Estonia earlier this year, Persson dismissed the idea that Swedbank, the largest lender in the three Baltic countries, would exit them.
"That hasn't even crossed my mind. It would not be better for these vulnerable countries if we, a responsible and serious bank, withdrew. We'll have to sort this out, this is our home market," Persson told a news conference.
Swedbank bulked up its board with three appointments at a extraordinary shareholder meeting, including the addition of Persson, as it seeks to regain investor confidence.
The 70-year-old former Swedish politician has emerged as a troubleshooter since playing an instrumental role in reviving Sweden's economy after a financial crisis in the 1990s.
Persson, a Social Democrat who served as prime minister for a decade until 2006 and has since sat on several boards including smaller regional lender Alandsbanken, vowed to restore confidence in Swedbank and work for a better corporate culture.
"We're going to clean our house. That work starts now," Persson said after his election as chairman of Swedbank, whose shares were up 1.3% to 140.70 Swedish crowns at 1300 GMT.
"What I can bring to the table is a long history of difficult economic-strategic decisions taken and many severe crises handled," Persson said.
Shareholders also voted in Bo Magnusson and Josefin Lindstrand as new members of the board, which also faces the task of finding a new chief executive for the bank.
Persson expects a new CEO to be in place by the end of autumn.
Anders Karlsson, acting chief executive, declined to comment on the state of the U.S. investigations. A note from KBW Europe said the market had priced in U.S. fines of $5 billion.
($1 = 0.8925 euros) (Reporting by Johan Ahlander and Esha Vaish in Stockholm; Editing by Johannes Hellstrom, Alexander Smith and Mark Potter)