In a nearly 3-minute video, Vitter said he believed that as governor "I can have a bigger impact" on the lives of Louisianans.
"As our next governor, I'll work to address the unique challenges and opportunities we face in Louisiana and help us reach our full potential," he said in the video posted on his campaign site, DavidVitter.com.
Current Gov. Bobby Jindal is barred from seeking a third term in the 2015 gubernatorial election because of term limits.
Vitter, elected to the Senate in 2004 after serving three terms in the U.S. House, said he would work to improve the state's education system, make the state more attractive to business and reform taxes.
He also said he would listen to the state's residents, "knowing I sure don't have the answers.:
"After listening ... and learning, I will lead," he said. "I am willing to take on the important issues and make the important decisions."
This would be his last political job, Vitter said, meaning "my only agenda is doing what's best for all Louisianans."