Shares of the London-based company were up 2.4% to $28.35.
Chief Executive Bernard Looney told employees in a global online call that the company will cut 10,000 jobs from the current 70,100, Reuters reported.
The affected roles will be mostly senior office-based positions and not front-line operational staff, the company said. The cuts would follow April's announcement of a 25% reduction in 2020 spending after the coronavirus pandemic brought an unprecedented drop in demand for oil.
BP and other energy companies have cut 2020 spending plans due to the outbreak.
"We will now begin a process that will see close to 10,000 people leaving BP - most by the end of this year," Looney said in a statement.
Looney blamed a drop in the oil price for the cuts, saying in an email to staff that "the oil price has plunged well below the level we need to turn a profit."
"We are spending much, much more than we make - I am talking millions of dollars, every day," the email said.
BP also said it would find $2.5 billion in cost savings by the end of 2021 through the digitalization and integration of its businesses.
The job reductions are part of Looney's drive to make the company more flexible as it prepares for the shift to low-carbon energy, Reuters said.
In February, Looney said that BP would invest more in low-carbon businesses and less in oil and gas over time.