The Anglo-Dutch giant's chief executive Ben van Beurden accepted that Arctic drilling "divides society", but said the world needs new sources of oil.
Greenpeace said Shell was taking a "massive risk" in a "pristine" region.
Shell also announced a $15bn (Â£9.9bn) cut in global spending, and profit figures that disappointed investors.
The cut in investment - spread over three years - comes after a fall in the oil price. Although the price is expected to remain lower in the medium term, Mr van Beurden said: "We are taking a prudent approach here and we must be careful not to over-react to the recent fall in oil prices.
"Shell is taking structured decisions to balance growth and returns."
Shell also said profits for the last three months of 2014 had risen to $4.2bn compared with $2.2bn in the same period a year earlier.
The numbers were below analysts' forecasts, prompting a big sell-off of Shell's shares, which were down by 4.3% at the end of Thursday.
Shell put its Arctic plans on hold two years ago after a drilling vessel ran aground and legal wrangles in the US.
The company has already spent $1bn on preparing its drilling work in Alaska's Chukchi Sea. It was costing Shell several hundred millions of dollars a year to keep the existing operations ticking over, the company said.
Mr van Beurden said there were still issues to resolve before drilling began, such as over operating permits and getting further facilities in place. But he hoped to see work begin in the summer.
"We will only do this if we feel that we can do it responsibly," Mr van Beurden told the BBC. "I think that we are as well prepared as any company can be to mitigate the risks."
He also pointed out that there are already other energy companies operating in the Arctic.
Mr van Beurden said that the world needs new sources of oil and gas to meet demand and that the Arctic offered potentially the biggest resource base ever found.
Estimates have put the estimates at some 24bn barrels in Alaska.
Environmentalists have campaigned against Shell for years. Greenpeace's Charlie Kronick, said: "Despite announcing cuts [in global investment], Shell hasn't taken the opportunity to cut its most high-cost high-risk project.
"Shell is taking a massive risk doggedly chasing oil in the Arctic, not just with shareholder value, but with the pristine Arctic environment.
"A spill there will be environmentally and financially catastrophic. It's time for investors to recognise that it's impossible for Shell to justify its continued pursuit of offshore Arctic oil."
As the first of the major oil companies to report its figures for last year, Shell plays the role of the canary in the coal mine - or on the oil rig.
After a rather sickly 2013, profits are actually up.
But the impact of the low oil price is clearly biting. The company announced that it would be cutting investment over the next three years in new exploration and the development of oil and gas fields, a move that will raise fresh concerns about its business in the North Sea.
Last summer Shell announced the loss of 250 jobs in Aberdeen.
The chief executive, Ben Van Beurden, said that the company would not "over-react" to the oil price which has fallen by 60% since last June.
And of course a low oil price means lower prices at the petrol pumps for consumers.
He said though that Shell would look at further cuts if necessary.
As well as the North Sea, the company's operations in Nigeria, where it recently paid a Â£55m bill to clean up pollution after a major oil spill, and the Arctic will also come under increased scrutiny.
Meanwhile, Shell's profits for the quarter after stripping out one-off items, such as asset sales and accounting changes, were $3.26bn. That is a 12% rise on the same period a year earlier but down from the $5.85bn in the June to September quarter.
Keith Bowman, equity analyst at Hargreaves Lansdown Stockbrokers, said: "As expected, fourth quarter performance has been impacted by the lower oil price, although downstream refining operations have provided some counterbalance.
"More broadly, the numbers are below forecast, with the news providing a difficult start to the oil majors' results season.
"In all, and despite the disappointing numbers, the dividend payment remains core, with the payment being left unchanged."
Shell said it was spending $12bn on dividends to shareholders in 2014, and also repurchased $3.3bn of its own shares.
The group said it had slowed the pace of share buybacks to conserve cash and that near-term oil prices would dictate how it progressed.
Oil prices have fallen by almost 60% since June because of weak global demand and a boom in US shale production.
Shell's main rivals, BP and Total, have also announced large cutbacks in capital expenditure in recent weeks.
Royal Dutch Shell is reviving plans to drill for oil in the Arctic in a move likely to intensify its battle with environmentalists.