Alexander, who has held the post nearly four years, announced his plans in a letter to colleagues Tuesday, The Washington Post reported.
Alexander, the third-ranking Republican in the Senate, was elected to a second term in 2008 and said he plans to run for re-election in 2014.
"Stepping down from leadership will liberate me to spend more time working for results on the issues I care most about," Alexander wrote.
"I want to do more to make the Senate a more effective institution so that it can deal better with serious issues. There are different ways to provide leadership within the Senate. After nine years here, this is how I believe I can now make my greatest contribution. For these same reasons I do not plan to seek a leadership position in the next Congress."
On the Senate floor Tuesday, he said he would be "more, not less aggressive on major issues" and noted 60 votes are needed to advance most legislation.
"The United States Senate requires 60 votes to achieve a result on serious issues and 60-vote results simply cannot be found among only Republicans, or only Democrats," he said.