Dinsmore will be responsible for the Scottish editions of the Sun, News of the World, Times and Sunday Times, and report to group general manager Will Lewis, who joined the company in July.
Rebekah Brooks, chief executive, News International said: "David has done a tremendous job as editor of the Scottish Sun, with sales now well above those of the Daily Record. This is a new senior role and is a well deserved promotion for David."
Dinsmore joined the Scottish Sun in 1990. He went on to become Scottish editor of the News of the World and later worked for both the Sun and the News of the World in London, before returning to the Scottish Sun as editor.
Dinsmore's replacement at the Scottish Sun will be announced shortly, News International said in a release.