The Nike "Swoosh" is a design created in 1971 by Carolyn Davidson, a graphic design student at Portland State University. She met Phil Knight while he was teaching accounting classes and she started doing some freelance work for his company, Blue Ribbon Sports (BRS).
BRS needed a new brand for a new line of athletic footwear it was preparing to introduce in 1972. Knight approached Davidson for design ideas, and she agreed to provide them, charging a rate of $2 per hour.
In June 1971, Davidson presented a number of design options to Knight and other BRS executives, and they ultimately selected the mark now known globally as the Swoosh. Davidson submitted a bill for $35 for her work. (In 1983, Knight gave Davidson a gold Swoosh ring and an envelope filled with Nike stock to express his gratitude.)
(All materials cited from an article on www.nikebiz.com called "Origin of the Swoosh.")
Much of the above information is corroborated on the Nike Canada official website.