The news agency's tally 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.
