Mohan is currently deputy editor of the tabloid newspaper and he replaces Rebekah Brooks (nee Wade).
Mohan has been deputy editor to Brooks since 2007 and has worked on the title for 13 years. He joined its showbiz column Bizarre from the News of the World, where he was a reporter.
Brooks' last day as editor of the newspaper before she takes up the role of chief executive of News International will be September 1.
James Murdoch, chairman and chief executive of Europe and Asia at News Corporation, said: "Dominic has proved himself a very capable deputy to Rebekah, sharing her passion for campaigning journalism on the issues that connect with the country.
"Under Rebekah's leadership, The Sun has gone from strength to strength, cementing its position as the most popular UK newspaper by taking share from rivals. I am very pleased to announce Dominic's promotion and look forward to seeing him build on that success."
Brooks said: "Dominic has been an outstanding leader at the paper, supporting me with energy and enthusiasm. He has an unrivalled understanding of what makes the paper tick and a real grasp of what makes a great Sun headline."
Mohan said: "I believe The Sun is the best paper on the planet. It is a privilege to take over as editor and I cannot wait to get started."
In the most recent ABC figures The Sun narrowly maintained its position as the UK's most popular daily newspaper, above its Sunday sister title The News of the World. The Sun's average circulation was 3,121,407 copies a day, down 0.4% year on year, but up 3.07% month on month.
Mohan was the favourite in the race to get the top job to which a number of big Fleet Street names were linked including Daily Mirror editor, Richard Wallace, Sun Online editor, Pete Picton, TheLondonPaper editor, Stefano Hatfield, current Sun Bizarre editor, Gordon Smart, and fomer News of the World editor, Andy Coulson.
The full list of runners and riders was according to Paddy Power as follows:
Dominic Mohan -- 1/7
Victoria Newton -- 10/1
Andy Coulson -- 12/1
Richard Wallace -- 13/2
Chris Pharo -- 14/1
Will Lewis -- 14/1
Colin Myler -- 20/1
Pete Picton -- 18/1
Col Allan -- 18/1
Gordon Smart -- 20/1
Tina Weaver -- 20/1
Dawn Neesom -- 33/1
Stefano Hatfield -- 40/1
Kelvin Mackenzie -- 50/1
Ellis Watson -- 100/1
Piers Morgan -- 100/1
Paul Dacre -- 25/1
Jeremy Paxman -- 500/1
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