The company is due to officially unveil the ads tomorrow but a report in the New York Times gives details of the campaign, created by Wieden & Kennedy in Portland, Oregon.
The ads see Agassi swap his racquet for a baseball bat while Williams takes up volleyball. Other stars in the ads are Marion Jones, who switches from athletics to gymnastics, and Tour de France-winning cyclist Lance Armstrong, who dons boxing gloves to take a turn in the ring.
The ad campaign carries the strapline "what if?" and will only be shown in the US and on . It is due to run for six weeks.
The Nike campaign is similar to the Adidas campaign that showed England football captain David Beckham and England rugby fly-half Jonny Wilkinson try out the other's sport. The ad ran in UK cinemas and on television from September last year and was created by 180 Amsterdam.
Nike has said that the ad was inspired by discussion among sports fans along the lines of "What if Tiger Woods' father had given him a baseball bat instead of a golf club?".
A spokeswoman for Nike Europe said: "We believe our spot is really unique because we haven't seen this insight being brought forward in any other campaigns."
The new advertising also harks back to a 1990s Nike campaign featuring the baseball and football player Bo Jackson trying his hand at activities including golf, tennis and guitar.
The London office of Wieden & Kennedy, Nike's award-winning agency, was accused of copying a Swiss film called 'Der Lauf Der Dinge' (The Way Things Go) when it created its groundbreaking "cog" ad for Honda last year. The creatives behind the ad admitted that it had been an inspiration and it raised questions about the advertising industry's habit of borrowing ideas.
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