Mohan replaces Rebekah Brooks (nee Wade), who moves to chief executive officer of the newspaper's publisher News International.
He starts the role on 2 September after Brooks edits her last paper on 1 September.
Mohan has worked at The Sun for 13 years, most recently as deputy editor and before that associate editor. He began as reporter on its showbiz column, Bizarre, before editing the column for five years from 1998.
Mohan, 40, moved to The Sun in 1996 from News of the World where he was a reporter.
The Sun is Britain's most popular newspaper, selling 3,121,407 copies a day.