Australia restricted New Zealand to 200 for nine before reaching 206 for four in 45.2 overs.
It was not all plain sailing for Australia, however, as New Zealand fast bowlers Kyle Mills and Shane Bond claimed a wicket each in the first three overs to leave the defending champions reeling on six for two.
With captain and leading run-scorer Ricky Ponting trapped lbw by the impressive Mills, who finished with three for 27, for just a single, Australia struggled to 37 for two after 16 overs.
But they wriggled off the hook as Watson, who scored 136 not out in the semifinal win over England, showed great composure before hitting successive sixes off spinner Jeetan Patel to end the match and finish on 105 not out.
Ponting was delighted his side had earned reward for their hard work since the Ashes defeat in England, and satisfied with such an emphatic showing.
"I´m ecstatic," he said. "To come away with a win and win a tournament as big as this one is great reward for all the guys, whether it´s coaches or players who have been around the group for the past six or seven weeks."
"It´s the second-biggest one-day tournament that you play, there´s nothing else outside a World Cup, so it´s a very special achievement."
New Zealand had a great chance to seize control in the 18th over when Cameron White, on 15, skied a pull off Ian Butler but wicketkeeper Brendon McCullum could not take the catch, which would have reduced Australia to 41 for three.
The Black Caps regretted the lapse by their stand-in captain, Daniel Vettori, having been ruled out of the final with a hamstring strain, as Watson and White (62) put on 128 for the third wicket.
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