She got 78 percent of the votes, while her rival, Bernie Sanders, could only manage 21.
The win propels Mrs Clinton into this week's crucial "Super Tuesday" voting in 11 states on a wave of momentum.
"Tomorrow this campaign goes national," she told cheering supporters.
Mr Sanders has congratulated her but said the campaign was just beginning.
With almost all the votes counted Mrs Clinton leads Mr Sanders by an almost 50-point margin.
Eight out of 10 black voters backed Mrs Clinton, exit polls suggested, a key section of the Democratic electorate.
