"Rather than producing tangible solutions to better this nation, partisan posturing has created a standstill," Alexander, 66, said in a statement.
He told The Monroe (La.) News-Star he never intended to be in Washington "all my life."
"I've represented the best people in the world; it's been a privilege and I've enjoyed it," said Alexander, who won his first congressional election in Louisiana's 5th District as a Democrat in 2002, beating Republican Lee Fletcher by fewer than 1,000 votes.
After changing parties in 2004, Alexander never faced a serious challenge again, winning a sixth term with 77 percent of the vote in 2012, Politico reported.
The chairman of the National Republican Congressional Committee called Alexander "a tireless and dedicated advocate for Louisiana families over a decade."
"I look forward to keeping the 5th District in Republican hands in 2014," U.S. Rep. Greg Walden of Oregon said.