England were bowled out for 249 in reply to Australia's 298 all out as the tourists signed off on a trip in which they have steadily improved with a decisive win.
QUICK SINGLE: Fifth ODI wrap
Watson's eighth one-day hundred was the decisive factor as Australia won their first trophy of an English summer in which they have contested the Champions Trophy, the Ashes and this five-match series.
During the trip they have had a change of coach and there were reports of discontent in the camp but Watson insists they are a happier squad now ahead of the upcoming tour to India and a home Ashes series.
Two matches were rained off but wins at Manchester and Southampton were enough for Clarke to get his hands on the silverware with Watson predicting more success to come under coach Darren Lehmann.
"We knew how important this game was and how important it was to come away with a series win. We had not had much success on this tour so far," Watson said.
"Things have changed quite a bit but the most important thing is that everybody is enjoying themselves. At the start of the tour we were not enjoying ourselves.
"We wanted things to change in a big way and for us to be more consistent. Everybody is excited."
Clarke praised Watson for showing his class at the end of a long and gruelling tour.
"We have worked extremely hard and this is a nice reward," Clarke said.
"I hope we put a smile on the faces of the Australian people watching us.
"It is about continuing to perform for this team. We want to be the No.1 one-day team in the world."
England were never up with the rate as Australia's bowlers kept them pinned down until Ravi Bopara and Jos Buttler had a brief flurry in the batting power play.
They took 26 off two overs but when Buttler went for 42 and Bopara for 62 the win was in the bag for the tourists.
England's reply had got off to the worse possible when Kevin Pietersen was run out for nought and George Bailey also pulled off a brilliant run out to remove Luke Wright with a direct hit from mid-wicket, while Joe Root dragged a wide one on from Mitchell Johnson.
"It was a challenging total and we lost wickets throughout the innings," England captain Eoin Morgan said.
Watson's century, against an inexperienced attack, was the bedrock of Australias total which looked to be heading beyond 350 when he and Clarke were batting.
They rushed the tourists score from 150 to 200 in just 32 balls and took a heavy toll on spinners James Tredwell, who went for 38 off four overs, and Root, who conceded 58 runs off six.
The pair's stand of 163 a record for one-day internationals at this ground kept England on the back foot until Clarke was caught at mid-in for off Chris Jordan.
Watson got to three figures off 87 balls but once he was out the runs dried up for Australia when they were looking to accelerate in the closing overs.