The news ends a month-long bidding war and comes just days after Anadarko's board said that Occidental, backed by billionaire Warren Buffet, had made a $55bn offer that was superior to that of Chevron.
The agreement reached between the groups following the first offer and dependent on the purchase of Anadarko Petroleum stipulates that Total will have to pay US$8.8 billion to Occidental Petroleum Corp for the group's African assets.
For Chevron's Wirth, the focus now shifts to what to do with the company's $74 billion pile of cash and unused shares.
"Winning in any environment doesn't mean winning at any cost", Wirth said in a statement.
Occidental Petroleum Corp. will hear directly from investors one day after clinching victory in the battle for Anadarko Petroleum Corp. and seeing its shares touch a new 10-year low.
Chevron said it will collect a $1 billion termination fee and plans to increase its share buybacks by 25%.
Berkshire said it will invest $10 billion in Occidental. Mizuho reiterated a "buy" rating and issued a $55.00 price objective on shares of Anadarko Petroleum in a research note on Tuesday, February 12th.
Buffett told shareholders at Berkshire's annual shareholders meeting Saturday that his company will engage in more such deals in the energy sector in the future.
It would make Occidental the third-largest USA oil company with a market value of about $80 billion, dwarfed only by global giants Exxon Mobil and Chevron.
The companies said the deal is expected to close in the second half of this year.
Buying Anadarko was seen as the best way for Occidental to gain more acreage in the Permian shale basin, where it markets almost a quarter of all barrels produced in the region.
She said the Anadarko deal represented a "transformational" opportunity for Occidental, telling Wall Street analysts the company has "a tremendous asset base with a huge upside".
Although acquiring Anadarko would have elevated Chevron's output into the realm of behemoths Exxon Mobil and Royal Dutch Shell, the combination may have challenged Wirth's commitment to his self-stated primary goals: expanding dividends and limiting debt.
Chevron shares rose 3.1 percent to $121.19 in mid-morning trading, while Anadarko fell 3.3 percent to $73.39 and Occidental sank 6.4 percent to $56.33.
Anadarko executives, however, remained concerned that Occidental shareholders could scuttle the deal, leaving them without a buyer, two sources familiar with the situation said. Buffett is known for moving quickly when a deal piques his interest, but he tends to avoid getting involved in hostile takeover bids.