Xerox Corp. agreed to buy Affiliated Computer Services Inc. in a deal valued at about $5.8 billion, making its biggest purchase to shift to technology services as sales of its printing equipment drop.  The acquisition will help triple sales from services to about $10 billion, Xerox said in a statement Monday. The total price of the cash-and-stock deal was about 34 percent more than Dallas-based Affiliated Computer’s stock before today’s trading.

Chief executive officer Ursula Burns, who took over in July, is increasing Xerox’s debt and more than doubling the workforce, sending the stock down and shaving about 10 percent off the purchase price. Her predecessor, Anne Mulcahy, helped Xerox avoid bankruptcy this decade by paring debt, exiting unprofitable businesses and shedding jobs.

“It’s going to take a Herculean effort to integrate these two companies,” said Peter Falvey, a managing director at Revolution Partners LLC in Boston. “There is significant execution and integration risk. It’s a very bold bet.”

Xerox, based in Norwalk, Connecticut, fell $1.30, or 14 percent, to $7.68 on the New York Stock Exchange, bringing the per-share value of the transaction to about $56.50, compared with $63.11 before Monday’s trading.

Affiliated Computer rose $6.61, or 14 percent, to $53.86, the biggest jump in two-and-a-half years. Affiliated Computer chairman Darwin Deason, the company’s founder, will become one of Xerox’s largest shareholders. He will receive about $800 million for his stake, including cash, Xerox shares and about $300 million worth of convertible stock.

The transaction helps Burns expand into a market Xerox values at about $150 billion and gives her a foothold in managing administrative operations for multiple arms of the US government. The number of workers at the world’s largest maker of high-speed color printers will increase to about 128,000.

“With this combination, our tool box just got a lot bigger,” Affiliated Computer CEO Lynn Blodgett said in an interview. Blodgett, 55, will run the business as a unit of Xerox and report to Burns, 51.

Almost 90 percent of Affiliated Computer’s new business contracts last year came from outsourcing, or managing operations for other companies. Total sales rose 5.9 percent to $6.5 billion in the year ended June 30.

Xerox has about 54,000 employees, and Affiliated Computer has 74,000 workers. Xerox said annual cost savings from the deal will increase to as much as $400 million in three years.

Xerox will pay $18.60 a share in cash and 4.935 shares for every Affiliated Computer share, amounting to about $56.50, based on Monday’s closing prices. Xerox also will assume about $2 billion in debt. Xerox had $1.22 billion in cash and cash equivalents at the end of last quarter, and about $6.7 billion in long-term debt.

Standard & Poor’s said it may cut Xerox’s BBB credit rating, citing the increase in debt. The rating is two steps above junk.

Mulcahy, who took over in 2001, had brought down the company’s debt from more than $18 billion the year before she took over. She cut at least 20,000 jobs to revive Xerox after the bursting of the technology bubble left Xerox with mounting borrowings and its first annual loss in five years.

Under Mulcahy, Xerox stopped making personal copiers and started focusing on laser printers, as well as color printing. Earlier this month, Xerox said it would begin selling digital printers for packaging and labels, aiming to tap a new market.

Deason said in the statement that he is “optimistic” about the combined company’s future and that he plans to remain a “long-term” investor.

In 2007, Deason and Cerberus Capital Management LP failed in an attempt to buy Affiliated Computer for $6.2 billion. The company’s independent directors alleged that Deason hampered their attempts to find better offers, a squabble that resulted in them resigning.

The recession may have hastened Xerox’s decision to expand in services as companies curbed spending for its equipment, said Falvey, whose investment bank worked with Xerox on a prior deal.

This month, Dell Inc. agreed to buy Perot Systems Corp. for $3.9 billion to expand into computer services. Last year, Hewlett-Packard Co. bought Electronic Data Systems Corp. for $13.2 billion in a similar deal.

“There’s just no question that some of these big guys are looking to become more horizontal,” said Falvey. Computer Sciences Corp. and some Indian outsourcing companies may become targets, he said.

Computer Sciences, the manager of networks for NASA and the US Navy, rose $2.41, or 4.8 percent, to $53.20 on the New York Stock Exchange. Cognizant Technology Solutions Corp., another provider of consulting and computer services, gained 84 cents, or 2.2 percent, to 38.65 on the Nasdaq Stock Market.

If Affiliated Computer walks away from the deal, the company will have to pay Xerox a termination fee of $194 million, according to a regulatory filing Monday. If Xerox backs out, it will owe Affiliated Computer $235 million.

Xerox will have to pay a fee of $323 million if the deal isn’t completed by June 27, 2010, and on that date all closing conditions except for financing requirements are satisfied.

JPMorgan Chase & Co., Blackstone Group LP and Simpson Thacher & Bartlett LLP are advising Xerox on the transaction, and Citigroup Inc. and Cravath, Swaine & Moore LLP are working with Affiliated Computer. Evercore Partners Inc. and Ropes & Gray LLP are counseling a special committee of Affiliated Computer’s board.