It involved the Gannet Alpha platform, 113 miles (180km) from Aberdeen.
The pipeline involved - which leaked more than 200 tonnes of oil - was about 300ft (91m) below the surface.
Shell admitted two charges relating to the incident at Aberdeen Sheriff Court. The BBC Scotland news website revealed last week the firm had been charged over the incident.
The court heard Shell's overall costs arising from this incident were estimated at about £45m, and the cost of replacing the pipeline was about £100m.
Paul Goodfellow, Shell's upstream director for the UK and Ireland, said: "We deeply regret the Gannet spill and accept the fine which has been handed down to us.
"We know that no spill is acceptable. Safety is at the heart of our operations and following this incident, a comprehensive review of our North Sea pipeline system was conducted.
"We have learnt lessons from this review and have applied them across our UK upstream operations."
WWF Scotland director Lang Banks said: "Despite being responsible for worst North Sea spill in a decade, the level of the fine is literally a drop in the ocean when compared to the billions earned by Shell annually.
"When it comes to protecting the marine environment and its own employees it's absolutely right that oil companies are prosecuted for their mistakes and that lessons are also learned by the wider industry.
"It's therefore disappointing that the fine was not much larger in this case."
Shell deployed a remotely operated vehicle to find the leak in the pipe flowing between an oil well and the platform.
The company shut off the well and depressurised the pipeline, stemming the flow of oil.
Work to release gas trapped in the pipeline was completed in November 2011.
Oil giant Shell has been fined £22,500 after a leak at a North Sea platform in 2011.