Two of the world’s top oil drilling companies, Transocean and GlobalSantaFe, said yesterday that they would merge to consolidate their position in a fast-growing market.

Under the terms of the cash-and-stock transaction, shareholders of Transocean and GlobalSantaFe will receive shares in a new company as well as $15 billion through a recapitalization plan. The combined company, which will be called Transocean, will have a global fleet of 146 drilling rigs and 20,000 employees.

The combination gives Transocean a 20 percent market share of drilling rigs like jack-up rigs, semi-submersibles and drill ships. The new company will own 48 units in the fast-growing segment of deepwater rigs able to drill in 3,000 feet of water or more. According to the consulting firm ODS-Petrodata, that would be one fewer than the combined deepwater fleets of their main rivals — Diamond Offshore Drilling, Noble, Seadrill and Ensco International.

Energy companies are scrambling to lock in offshore rigs to drill in the current high-price environment. Drillers have been struggling to meet demand, with waiting periods sometimes stretching into years.

Analysts say that most large American drillers have been slow in expanding their fleets. Together, Transocean and GlobalSantaFe have only five rigs under construction, out of a total of 138 being built.

“They are going to lose market share as a result of this rig-building boom unless they acquire some other rigs under construction,” said Tom Kellock, the head of consulting and research at ODS-Petrodata.

Given the tightness in the global drilling market, rig prices have more than doubled in recent years. They now reach $500,000 a day at the most challenging deepwater wells in the Gulf of Mexico or West Africa.

Robert L. Long, the chief executive of Transocean, who is to have a similar position at the new company, said, “We will be positioned to better offer the full scope of drilling services to customers in all geographical areas.”

Together, the merged companies have a $33 billion backlog of contracts extending as far as 2015.

GlobalSantaFe’s chairman, Robert E. Rose, will serve as chairman of the successor company, and Jon A. Marshall, GlobalSantaFe’s chief executive, will become its president and chief operating officer.

The combination will allow Transocean to expand its presence in the Middle East and take advantage of existing contracts between GlobalSantaFe and state-owned oil companies including the world’s biggest oil concern, Saudi Aramco.

“The combined company will have a broader customer base,” Mr. Marshall said, “particularly with the increasingly important national oil companies.”

Transocean stockholders will receive $33.03 in cash and 0.6996 share of the combined company for each of their shares. GlobalSantaFe shareholders will receive $22.46 in cash and 0.4757 share for each share they now own.

The transaction provides no premium for shareholders of either company.

Transocean’s market capitalization, after the close of trading Friday, was about $32 billion, nearly twice GlobalSantaFe’s value of $17 billion. The new company will have an enterprise value of $53 billion. (Enterprise value is a measure of what the market estimates a company’s continuing operations to be worth. It is equal to its market capitalization, plus preferred stock and debt.)

The transaction is expected to be completed by the end of the year. Each company is to have seven directors on the new board.

In trading yesterday, shares of Transocean rose $5.99, or 5.4 percent, to $115.96. The stock has more than quadrupled over the last three years. GlobalSantaFe shares rose $3.59, or 4.8 percent, to $78.33. It has more than tripled in three years.

The cash for the payment to shareholders will come from a bridge loan from Goldman Sachs and Lehman Brothers. Both also acted as financial advisers, Goldman to Transocean and Lehman to GlobalSantaFe.

Baker Botts was Transocean’s legal adviser, while the law firm of Skadden, Arps, Slate, Meagher & Flom advised GlobalSantaFe.