The PC maker said it plans to buy shares on the open market from time to time depending on market conditions.
"At current price levels, we believe Compaq's stock offers a tremendous investment opportunity for the company," Michael Capellas, Compaq's chief executive, said in a statement.
Compaq's stock was up $1.05, or almost 5 percent, to $22.55 in early trading Friday. The company's shares have traded from $34.87 to $18.16 in the past 52 weeks.
On Thursday, Capellas issued a memo to employees in an attempt to calm worries about the jittery PC market, which has been rocked by falling stock prices.
In the memo, obtained by CNET News.com, Capellas told employees: "There is continued volatility in the market today, particularly in technology stocks, and I know this creates a lot of uncertainty for employees."
Capellas wrote that he believes increased price competition and slower PC sales are "short-term issues" and that he does not expect consumer spending on technology to slow down over the long term.
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Discuss: Compaq to buy back up to $1 billion of shares
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