He made the announcement in a speech to workers at a car factory in the Volga city of Nizhny Novgorod.
"I will put forward my candidacy for the post of president of the Russian federation," he said.
Mr Putin has been in power since 2000, either as president or prime minister. If he wins the March election, he will be eligible to serve until 2024.
Russian TV journalist Ksenia Sobchak has already said she will stand in the election but opinion polls suggest Mr Putin will win easily.