The acquisition is being carried out through the much bigger New England Electric System, which National Grid agreed to buy in December for $4.6bn.
The purchase price is $31 a share - a 23 per cent premium to EUA's price in early December before merger speculation began.
National Grid is paying $634m for EUA and assuming a further $365m in debt.
However, National Grid is expected to recoup about $180m through sales of unwanted assets such as EUA's combined heat and power generating plants.
Analysts estimated that National Grid would realise savings of at least $25m a year by merging the transmission and distribution businesses of the two companies, which operate next to each other in the north-east region of the US.
National Grid said it hoped to receive regulatory and shareholder approval for both the US acquisitions by early 2000.
The aim is to complete the two deals on the same timetable.
EUA has 300,000 customers and made net profits of $40m on revenues of $569m in 1997. New England Electric System has 1.35 million customers.
At the time of the NEES deal, National Grid's chief executive, David Jones, made it clear that it was on the lookout for further acquisitions. He said the EUA deal was fully in line with that strategy.Reuse content