Mr Marr, aged 36, was among the journalists who joined the paper before its launch in 1986, as a founding member of its political reporting team.
He left in 1988 to work as the political editor of The Scotsman, and then moved on in the same role to The Economist.
He returned to The Independent in 1992 as chief political commentator, in which role he was awarded Columnist of the Year in the British Press Awards 1994, and also the What The Papers Say columnist award for the same year.
He has published two books of political commentary: The Battle for Scotland in 1992, and Ruling Brittania last year.
"I cannot think of a more exciting job at a more exciting time," he said yesterday. "Britain is about to go through a period of extraordinary change, and The Independent will be in the middle of the action.
"The paper is already brimming with talented writers. Over the next few years we will make it a showcase of the best of British journalism."
Colin Hughes, formerly managing editor, and also a member of the paper's launch team, is appointed deputy editor.
Charles Wilson, group managing director of Mirror Group Newspapers, has been the acting editor since last November. He has been appointed to the board of Newspaper Publishing, the company that owns The Independent.Reuse content