In a project which will last 10 years, the firm plans to use the specially built £2.4bn Pioneering Spirit to carry out the major engineering challenge on its oil and gas field, located 115 miles northeast of the Shetlands.
The Pioneering Spirit is 382 metres long and 124 metres wide and is being made ready to sail from Rotterdam port to lift and remove the "topside" of the first of four oil rigs in the field.
Once free of the rig legs, the platforms weighing as much as 30,000 tonnes are being transferred to Teeside where they will be scrapped in a custom-built yard near Hartlepool.
The Brent field is one of the largest fields in the North Sea and is responsible for about 10% of total North Sea production during the past four decades.
At its peak, the four rigs were pumping 500,000 barrels of oil out of 154 seabed wells every day.
Decommissioning the field will be a major infrastructure project and is being closely watched by the industry because it is the biggest North Sea field to be dismantled so far, with hundreds more to follow.
It is also being closely watched by environmental groups who have already expressed concerns about Shell's planning process.
WWF Scotland and seven other environmental organisations have claimed the oil giant's proposals contain "insufficient information" and could breach international rules.
Such rules state all oil rig elements must be removed once a platform has finished work but exceptions can be made in certain circumstances.
Shell's plan, which is being considered by the international regulator, is to leave the concrete legs of three of the four decommissioned rigs on the seabed.
Lang Banks, of WWF Scotland, said: "There are very clear international rules setting out what Shell have to do in order to prove their case to leave these materials on the seabed.
"Unfortunately in this case we don't believe Shell have adhered to those rules and they're going to have to go back and think again.
"That means what we're saying is we're rejecting Shell's plans and they're going to have to go back and think."
The company argues the safety risks associated with trying to remove the concrete legs outweigh "minimal environmental benefit".
Duncan Manning, head of Shell's Brent field decommissioning, told Sky News: "There are significant technical difficulties with removing the rig infrastructure.
"We need to balance up an holistic range of factors looking at not just the impact to the environment but also the impact to society, safety, feasibility and costs."
The row comes 20 years after Greenpeace led a high-profile campaign against Shell's plans to decommission another part of the Brent field - Brent Spa.
Protests and boycotts at Shell's petrol pumps forced the company to change plans and it says it has learned from the experience.
Environmental groups argue that leaving the rig structures could pollute the water and harm marine life, but some research suggests the solution could be beneficial.
Environmental litigation and liability expert Helen Bowdren said the approach "can actually have some environmental benefits".
"For example, you might get sea life being able to utilise the installations and build coral on it.
"So the environmental debate has moved on quite a lot recently and many people think that actually removing the installations comes with more environmental harm than leaving them in place."
The first rig "topside" will be removed in early May and transferred to Teesside.