(Adds details on Vitter's legislative record, potential opponents; Changes headline)
By David Lawder and Doina Chiacu
WASHINGTON, Jan 21 (Reuters) - Republican U.S. Senator David Vitter announced plans on Tuesday to run for governor of Louisiana in 2015, saying that he thinks he can help the people of his state more from the governor's office than from Capitol Hill.
"I believe that as our next governor, I can have a bigger impact addressing the unique challenges and opportunities that we face in Louisiana - helping us fully reach our full potential," the social conservative said in a YouTube video announcing his candidacy.
If successful, he would replace current governor Bobby Jindal, who has run up against term limits and is viewed as a potential candidate for the Republican presidential nomination in 2016.
Vitter, 52, intends to stay in the Senate while he campaigns for Louisiana's top office, his spokesman said. That would ensure his decision will not affect the Senate's balance of power in the 2014 congressional elections in November.
Democrats currently control the Senate, 53-45, plus two independent senators who caucus with the Democrats.
Vitter's second, six-year term expires at the end of 2016.
Vitter said he has been preparing for his gubernatorial run with a series of town halls and other meetings across the state and pledged to improve education and make Louisiana more attractive to growing businesses.
"We'll do it by reforming taxes and spending, spurring economic growth and creating budget stability," he said, adding that governorship would be his "last political job, elected or appointed."
Vitter weathered a sex scandal during his first term and won re-election in 2010. In 2007, he admitted to "a very serious sin" and apologized after he was linked to a Washington escort service.
Vitter's phone number was found five times in phone records dating from 1999 to 2001 for "D.C. Madam" Deborah Jeane Palfrey, who is accused of running a prostitution ring in Washington, the New Orleans Times-Picayune reported at the time. Palfrey has said she operated a legal escort service.
Vitter said at the time he and his wife confronted the issue and sought marriage counseling. He accused enemies of dredging up the scandal to hurt him.
The allegations stunned many in Louisiana because Vitter, a Harvard graduate and Rhodes scholar, was a highly visible social conservative who championed family values and ardently opposed abortion and gay marriage.
CONSERVATIVE BILLS, NO LAWS
Last year, Vitter introduced more bills - 67 - than any other member of Congress, but none were enacted into law, according to Govtrack.us, an independent political tracking website. Many of the proposals reflected conservative political causes, including restrictions on abortions and prohibitions on regulation of U.S. carbon emissions.
During the autumn battle over the government shutdown, Vitter gained notoriety for proposing that members of Congress, their staffs and top Obama administration officials be required to purchase health insurance on the so-called "Obamacare" exchanges with no subsidies, arguing that this was a hardship that would prompt Congress to change the healthcare reform law.
His proposal was not adopted, but some lawmakers are voluntarily buying insurance on the Affordable Care Act exchanges.
To win the governorship in 2015, Vitter would have to defeat a declared Republican opponent, Lieutenant Governor Jay Dardenne. Republican state Treasurer John Kennedy also has said he is considering entering the race.
On the Democratic side, state Representative John Bel Edwards has declared his candidacy. Many in the state also are watching to see whether popular New Orleans Mayor Mitch Landrieu decides to run.
Landrieu, a Democrat who has presided over the city's rebuilding after a devastating 2005 hurricane, is expected to win a third mayoral term on Feb. 1, with an endorsement from President Barack Obama. He is the brother of Louisiana's Democratic senator, Mary Landrieu, who also is seeking re-election in November.
LaPolitics.com, a state political website, in December reported poll results showing that Vitter would lead a theoretical three-way race with Landrieu and Dardenne, with 35 percent of the vote.
In Louisiana's open primary system, all candidates run together in a single election. If one fails to reach a majority, a runoff is held between the top two vote-getters, regardless of party affiliation. (Reporting by David Lawder; Editing by Amanda Kwan and Jim Loney)