The count puts Mrs Clinton on 2,383 - the number needed to make her the presumptive nominee.
She will become the first female nominee for a major US political party.
But rival Bernie Sanders said Mrs Clinton had not won as she was dependent on superdelegates who could not vote until July's party convention.
Mrs Clinton reached the threshold with a big win in Puerto Rico and a burst of last-minute support from superdelegates, AP said late on Monday night.
Superdelegates are party insiders who can pledge their support for a candidate ahead of the convention but do not formally vote for them until the convention itself.
AP's announcement came ahead of Democratic primaries on Tuesday in California, Montana, New Mexico, North Dakota, South Dakota, and New Jersey. Polling stations opened at 06:00 local time (10:00 GMT) in New Jersey. The last ones to close will be in California at 03:00 GMT Wednesday.