Kelner, who previously edited the newspaper between 1998 and 2008, is taking the role on an interim basis as a full time editor is sought. Roger Alton confrmed he is leaving the newspaper.
John Mullin, editor of the Independent on Sunday, will take on additional duties on the daily and advance the integration of the two papers, according the The Independent.
Alton said standing down was the right thing to do, following the sale of the paper.
Replacing him is the first major strategic decision taken by the paper's new Russian owner Alexander Lebedev, who acquired the Independent and the Independent on Sunday for a nominal £1 last month.
As part of the restructure, Geordie Greig, the current editor of the Evening Standard, will take on the enlarged role of editorial director across the Evening Standard and the Independent's two titles. He will maintain his role as editor of the Standard.
Kelner will report to the board of Independent Print Limited, the vehicle founded by Alexander Lebedev to house the papers he bought from Independent News & Media, which consists of Greig, Alexander's son Evgeny Ledebdev and Justin Byam Shaw, the chairman of the London Evening Standard.
Roger Alton, 62, joined The Independent from The Observer, where he had also been editor. Prior to that, Alton spent 20 years at The Guardian.