The best expression is: 'It has a twenty-year history.' Note that that 'twenty-year' is used as an adjective here, and the word 'year' is in the singular. Not 'years', but 'year'.

You could also say : It has a/an x-year history e.g. a 20-year history. They both mean the same but this version is more concise.

You would say "It has a history of ... years"