The oil giant also expects to streamline its portfolio by selling between $15 billion and $20 billion of assets.
The combined company will remain far behind Exxon Mobil Corp. and Royal Dutch Shell Plc.in market capitalisation, but Chevron will jump from being the world's fourth biggest energy producer, to second, according to Wood Mackenzie.
The transaction will give the second biggest US energy company a boost in shale oil production as well as natural gas.
Some of Anadarko's assets may be sold after the deal closes, the company said. It estimates that the combined company can drive out $1 billion in annual costs.
The acquisition is composed of 75 percent stock and 25 percent cash, with Anadarko shareholders receiving 0.39 shares of Chevron and $16.25 in cash for each Anadarko share held.
Shares of Anadarko jumped 32% at the opening bell Friday, while Chevron's stock fell 5.3%.
As oil companies have become more efficient at producing shale oil, which has changed the global equation by making USA oil a rival against the cheap oil produced by Organization of the Petroleum Exporting Countries. Exxon had average production a year ago of 3.833 million.
"This takes a great company and makes it even better", Chevron's Chairman and CEO Michael Wirth told CNBC's "Squawk Box" immediately after the news broke. Chevron will assume $15 billion of Anadarko's debt.
Chevron, which already has 2.3 million acres in the Permian Basin, said the combined company would have a 75-mile (120-km)-wide corridor across the Permian's DE basin, on the Texas-New Mexico border.
"It creates attractive growth opportunities in areas that play to Chevron's operational strengths and underscores our commitment to short-cycle, higher-return investments", Wirth added. Widening the measure to include chemicals and state-owned companies, both would be eclipsed by Saudi Aramco's US$69 billion acquisition of a majority stake in local petrochemical company Sabic this year.
The Chevron executive is detailed-oriented and a relentless worker, said Mike Sommers, president of industry group American Petroleum Institute, where Wirth is a member of the executive committee. Anadarko has a "world-class resource base in Mozambique", Chevron said.
Chevron said the combined entity would have had daily output of 3.596 million barrels equivalent of oil previous year, compared with Shell's 3.666 million.
The deal, which is subject to shareholder and regulatory approval, is expected to close in the second half of 2019.
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 expects the deal to add to free cash flow and earnings per share one year after closing, at US$60-a-barrel Brent.
Head of research, Per Magnus Nysveen said: "We think the deal value price of $50 bn is surprisingly good for Chevron, as our base case valuation of Anadarko is $65 bn".
Credit Suisse Securities is Chevron's financial adviser, while Paul, Weiss, Rifkind, Wharton & Garrison is its legal adviser.