NEW YORK (Reuters) - Verizon Wireless said yesterday it would buy rural mobile service provider Alltel Corp for $28.1 billion including debt, which would vault it to first place in the US market ahead of AT&T Inc.

Under terms of the deal, Verizon Wireless would acquire the equity of Alltel for $5.9 billion and assume an estimated $22.2 billion in debt, incurred primarily when Alltel was taken private in a leveraged buyout last November by TPG Capital and Goldman Sachs Group Inc's GS Capital Partners.

Shares of Verizon Communications Inc, which owns 55 percent of Verizon Wireless, rose more than six percent after the news, as the company said it would boost its earnings by more than 10 cents a share in the first year after the deal, excluding items such as integration costs. Shares of Vodafone Group Plc, which owns the remaining 45 percent of Verizon Wireless, rose 3.8 percent.

"This is a way of getting growth from a market that's becoming fully saturated and beginning to slow down," said analyst Joseph Bonner at Argus Research.

"They get the bragging rights," he said, referring to Verizon overtaking AT&T as the largest player in the US mobile services market.

Verizon Wireless said the deal would generate savings of $1 billion in the second year after closing, which is targeted for the end of 2008, pending regulatory approval. It forecast total savings of more than $9 billion by 2011, driven by reduced capital and operating expenses.

Verizon said the deal would be cash-flow positive in the first year, though it estimated integration costs at $1.1 billion to $1.2 billion in the first year and $500 million to $600 million in the second.

Verizon said it agreed take on about $5 billion in bridge loans before the deal closed as part of the agreement. It would buy the loans at a discount of $200 million compared with face value, a person familiar with the deal said.

Verizon Wireless does not expect to pay a dividend to Vodafone for the next three years, as the company would use its cash to pay off debt from the deal. It said it would review the process annually.

Verizon's move comes about seven months after Alltel's $27.5 billion leveraged buyout, which was the largest-ever private equity investment in the US wireless industry.

Analysts have speculated that TPG and Goldman may have wanted to sell Alltel because of tight capital markets.

"All of the investment banks have constrained balance sheets right now and they need to free up their capital. Alltel was bought at a pretty heady time in the credit market," said Yvonne Bishop, assistant portfolio manager at Summit Investment Partners, which owns Verizon shares.

Verizon Wireless and Alltel, which has more than 13 million customers, together would have more than 80 million customers. AT&T, currently the biggest US wireless service, said it ended the first quarter with about 71 million customers.

Alltel serves 57 primarily rural markets where Verizon Wireless does not operate, Verizon Wireless said. They both use a common network technology.

"We took a risk that, rather than overpaying, there would be a better day," said Verizon Communications chief executive Ivan Seidenberg about why the company was buying Alltel now rather than last year, when it went on the market. He said he approached the private equity owners about the deal in April.

Verizon Wireless and Alltel have an overlap of about 15 percent of their network coverage, according to Seidenberg. But he said that did not necessarily correspond exactly to the amount of divestitures regulators would require. He said he expected any divestiture requirements to be "manageable".

The companies have agreed on a break-up fee of about $500 million, Seidenberg told analysts on a call.

Vodafone executives said on a separate call that holding onto its Verizon Wireless stake was the best way to draw value from the investment and that the deal was expected to immediately add to its adjusted earnings per share. Vodafone has frequently come under pressure from investors to cash in on Verizon Wireless.

Verizon Wireless said Morgan Stanley acted as financial adviser for the deal and would provide bridge financing. Citibank, Goldman Sachs and RBS advised the sellers, it said. UBS advised Vodafone in the deal.

Verizon Communication shares were up $2.40, or 6.5 percent, at $39.38 on the New York Stock Exchange in afternoon trading. Vodafone shares rose 5.8 pence, or 3.75 percent, to 155 pence in London.