Mr Dudley has also thrown his support behind the use of controversial fracking techniques in the UK but said BP would not be involved because it "would attract the wrong kind of attention".
BP had a tough end to 2013, it revealed yesterday, as underlying replacement cost profit for its fourth quarter dropped to $2.8 billion (£1.7bn), down $1.8bn on the same period last year.
Full-year earnings for 2013, before exceptional items, were down 21.6% at $13.4bn.
Mr Dudley said: "Aberdeen was and still is in many ways the heartland of the offshore oil and gas industry."
He said it remained an important centre of innovation for the industry.
BP has operated in the North Sea since the 1960s but as part of a wider scaling back of its operations after the 2010 Gulf of Mexico disaster it sold a number of interests including the $1bn disposal of its interests in several central North Sea oil and gas fields to Abu Dhabi's Taq at the end of 2012,
Mr Dudley said: "We have got a number of large, profitable protects that are under development."
He highlighted the Greater Clair area, west of Shetland, where the first oil is expected from the £4.5bn Clair Ridge development in 2015. A third phase is also mooted.
He said the Quad 204 project to replace equipment at the Schiehallion field west of Shetland was also significant.
BP confirmed plans to bring the Kinnoull field north-east of Aberdeen into production this year.
"These are high-margin projects. They are very important. They will keep production in the UK going past 2050 but the UK as an oil province is definitely over its peak. It is in its very mature phase," he said.
Mr Dudley called on the UK to get behind the controversial fracking industry. Shale gas production has slashed energy prices in the United States but there has been little exploration in the UK, despite Government support.
He said: "It would seem absolutely right to me for the country to see if it has shale gas."
Prices for gas and electricity in Europe are three times higher than in the US, giving North America an economic advantage, he argued.
During fracking water, sand and chemicals are injected to fracture underground rock formations. Critics claim it can spoil water supplies.
Mr Dudley said BP would not participate in the UK industry.
"We are not involved. We think we would attract the wrong kind of attention," he said.
After selling another $17.1bn of assets last year, BP has raised the $38bn it targeted in an effort to slim down following the 2010 Gulf of Mexico disaster. "We are a much smaller company than we were in 2010," Mr Dudley said.
Another $10bn of asset sales are planned for the next two years with much of the proceeds pencilled in for share buy backs.
BP has now taken provisions of $42.7bn for the Gulf of Mexico oil spill, although the bill could rise if it loses some key court cases.
Before the Deepwater Horizon disaster BP was producing 4bn barrels of oil a day. This dropped to 2.25bn but is now up to 3.2bn due in part to its 19.75% stake in Russia's Rosneft, which has ambitions to extract oil from the Arctic.
Mr Dudley said BP would consider working with Rosneft on some onshore projects.
He sought to reassure investors concerned that oil companies prioritise investment over pay-outs.
"We treat our projects as if we are portfolio managers for our shareholders," he said.
BP's shares closed up 0.2p or 0.04% at 473.8p.