Things become history when historicised by historians. For what is historicisation and who is a historian see another answer at http://history.stackexchange.com/questions/11700/what-are-some-indicators-that-distinguish-pseudo-history-from-actual-history/11721#11721What are some indicators that distinguish pseudo-history from actual history?
The largest element of this is access to the documentary records of the past. Some documentary records are held orally, and these become accessible when people start to memorialise their own past. The largest source for the documentary record of the past is archives. The largest archives tend to be state archives. State archives make documents accessible after 20 years, or 30 years, or 50 years or never. (For example: https://www.nationalarchives.gov.uk/about/20-year-rule.htm)
Some archives become open to historians much sooner. Failed states tend to be unable to protect their archival heritage, and the states that come later tend to make these open. Occasionally individuals release large slabs of state documents. Private organisations may release archival material earlier, or later. Or a failed organisation may suddenly release recent information.
Due to the role of the state in supervening people's lives, and as a direct participant in social action, state archives tend to dictate the ebb and flow of historicity. So "enough time to research a journal article or book" after an archival opening is a good guess. Say 20-25 years.
Things that are historical can still be current events. History is often used in contemporary politics for effect.