Chevron, which already has 2.3 million acres in the Permian Basin, said the deal to buy Anadarko would give the combined company a 75-mile (120-km)-wide corridor across the Permian's DE basin, on the Texas-New Mexico border.
The premium is high compared with most other acquisitions of oil companies valued at more than US$1 billion.
Occidental Petroleum Corp, another company with assets in the Permian, bid more than $70 per share for Anadarko and is now considering options, sources said.
Chevron shares fell 4.9 percent to $119.76 on Friday.
Analysts have painted Anadarko as a potential target for giant oil companies for years, arguing that the company's drilling projects in the US and overseas could be enough to bring offers to the table.
Anadarko Petroleum stock opened at $61.78 on Friday.
With oil prices surging this year, Chevron and larger rival Exxon Mobil Corp have been increasing investment in the United States' Permian basin in West Texas, the most prolific shale oil field in the country.
"Consolidation in deep water and the shales makes complete industrial sense", Christyan Malek, head of EMEA oil and gas research at JPMorgan, said by email.
By combining the companies, Chevron expects to cull $1 billion in costs. "It gives the combined entity the ability to high-grade its assets and focus on where the best cash returns are".
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Anadarko submitted the second most applications for permits to begin drilling in Wyoming past year, but it trailed behind in actual production.
The deal may put pressure on Shell to seek assets in the Permian, where the Anglo-Dutch company has said it wants to grow.
The acquisition consideration is structured as 75 percent stock and 25 percent cash, providing an overall value of US$65 per share based on the closing price of Chevron stock on April 11, 2019. Oil executives and bankers had in the past speculated that Shell may buy Anadarko, because they have adjacent acreage.
The two combined companies will produce about 3.6 million barrels a day, or 5% less than Exxon and similar to the output of other giant oil companies like Royal Dutch Shell PLC and BP PLC.
Anadarko shareholders will receive 0.38 shares of Chevron and $16.25 (£12.43) in cash for each of their shares.
Chevron's pledge to restrain expenditures has made it a favorite among energy stocks, with its shares up 13.8 percent this year.
"Clearly, a large driver of the deal is Anadarko's prized position in the Delaware Basin where Chevron increases its position by 240K net acres to over 1.4M net acres", says Drillinginfo's Andrew Dittmar. As a group, equities analysts expect that Anadarko Petroleum will post 1.66 EPS for the current fiscal year.
The transaction has been approved by the Boards of Directors of both companies and is expected to close in the second half of the year, according to the statement.
Chevron was advised by Credit Suisse Securities. Evercore Inc. and Goldman Sachs Group Inc. advised Anadarko alongside law firms Wachtell, Lipton, Rosen & Katz and Vinson & Elkins LLP.