Shell said the the sale of 71.6 million shares would produce pre-tax proceeds of about $US1.7 billion (A$2.2 billion).
The sell-down capitalises on recent strength in Woodside's share price, which has been buoyed by the higher oil price.
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According to DXC's corporate profile, the company has 155,000 employees in more than 70 countries, serving some 6,000 clients. The company also will work with the state-backed Louisiana Economic Development's FastStart workforce development program.
Earlier Monday the company had said it would sell the smaller stake for approximately $1.7 billion.
Originally, Shell it agreed to retain a 4.8% stake but such was the demand it chose to sell the whole lot to raise US$2.7bn (A$3.5bn).
In November 2010, it sold 10 percent of the issued capital of Woodside, taking its stake to 24.27 percent.
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After being diluted further because of a decision not to participate in Woodside's dividend reinvestment programme, and what Shell said was a "change in Shell's level of involvement over Woodside's financial and operating policy decisions", management concluded a year ago that Shell "no longer [had] significant influence".
Shell said today that proceeds from its sale of Woodside shares will be used to reduce the group's net debt.
"Woodside will maintain a close working relationship with Shell - as a joint venture partner and customer of Shell technology - and we recognise that Shell will always be part of our history", Woodside Chief Executive Peter Coleman said in a statement.
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But "this one is for the kids" Mr Constance reiterated on Monday. Over 15,000 different names were submitted to the competition.
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