Profit after tax stood at USD 115 million (108 million euros) compared with a net loss of USD 6.5 billion in 2015, BP said in an earnings statement.
BP took another huge charge linked to its role in the 2010 Gulf of Mexico oil spill -- but at USD 4.0 billion it was lower than in 2015.
The latest charge brought the overall cost to BP to around USD 63 billion, or USD 44 billion after tax.
"We have adapted by cutting our controllable cash costs by USD 7 billion from 2014, a full year earlier than planned.
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"Continued tight discipline on costs remains essential. Everything we have done during the year has made us a more resilient and competitive company," he added.
In 2015, BP posted the company's biggest loss in at least 20 years, ravaged by Gulf of Mexico spill costs and tumbling oil prices -- which caused the group to axe jobs and cut investments.
"With our Deepwater Horizon financial liabilities now substantially behind us, BP is fully focused on the future," Dudley added Tuesday after a year in which BP was hit hard also by weak oil prices despite a market recovery in the fourth quarter.
BP noted that average Brent North Sea crude prices stood at USD 44 a barrel in 2016, the lowest for 12 years.
Crude prices have however rebounded sharply in recent months, with Brent back above USD 55 thanks to a deal by OPEC and non-cartel members to limit output.
In morning deals following the update, BP's share price dropped 2.4 per cent to 464.80 pence on London's benchmark FTSE 100 index, which was up 0.4 per cent overall.
"BP needs oil to fetch USD 60 a barrel this year to effectively break even, and with Brent currently trading at around USD 56, it is still dependent on fair winds from the commodity markets to push it along," Laith Khalaf, senior analyst at Hargreaves Lansdown stockbrokers, said in reaction to today's results update.