The move will add a central North Sea hub to Taqa's UK presence and the company said it secures the future of 2000 jobs.
Meanwhile, the sale will help BP meet the billions of dollars in costs it faces from the 2010 Gulf of Mexico oil spill.
Taqa chairman Hamad Al Hurr Al Suwaidi, a member of Abu Dhabi's executive council, said: "This investment shows our commitment to the future of the North Sea. It is underpinned by the UK Government's commitment to long-term fiscal stability."
Bob Dudley, BP chief executive, said: "This transaction is in line with BP's strategy to focus on a smaller number of higher-value assets with long-term growth potential and to continue the simplification of our portfolio with a further reduction of operated infrastructure and wells."
Taqa will buy a number of central North Sea oil and gas fields for $1.058bn plus future payments dependent on oil prices and production, which could reach another $250m over the next three years.
A deposit of $632m (£398m) has been paid.
The assets included in the sale are BP's interests in the BP-operated Maclure, Harding and Devenick fields, and its stakes in the Brae complex of fields and the Braemar field – operated by other companies.
The sale is subject to regulatory approvals and is expected to complete in the second quarter of 2013.
Taqa has an established position in the northern North Sea and the purchase will add a second major development hub in the central North Sea to the business. Last month Taqa reported that a well drilled from the North Cormorant platform had encountered a major find.
The BP acquisition is expected to increase Taqa's net production by approximately 21,000 barrels of oil equivalent per day (boed), on top of current production of some 43,000 boed.
Taqa said the deal secures the future of 2000 workers at its North Sea operations, including 400 who are employed directly.
The deal consists of a 70% interest in the Harding field, 37.03% in Maclure and 88.7% in Devenick in the central North Sea.
Taqa will also increase its non-operated interests in the Brae area and associated infrastructure including the Forties-Brae and Forties-Braemar pipelines.
BP has now entered into agreements to sell assets worth around $37bn since the beginning of 2010, close to its target of $38bn.
It has now sold $2.8bn of assets in the North Sea including non-operated stakes in the Draugen, Alba and Britannia fields.
Trevor Garlick, BP's regional president for the North Sea, said: "BP continues with a focused investment programme in the UK and Norway, which includes planned capital spending of $10bn over five years."
Leo Koot, managing director of Taqa's UK operations, said: "This will provide us with new exploration and development opportunities in the central sector of the UK North Sea.
"We are confident we can safely generate significant value from these assets over many years to come."
The deal comes at a time when advances in technology have transformed the prospects of some fields that were previously considered uneconomic.
Earlier this week Scottish Enterprise portrayed a positive future for the North Sea with 86 new fields on the UK Continental Shelf under development or expected to see work begin before 2016.