The 190p-a-share offer is a 15 per cent premium to the American Port Services share price on 6 May, a day before ABP announced it was in talks to buy the London-listed port operator at that price.
For ABP, the move is the latest in a series of measures to boost returns, promised by managing director Andrew Smith, who joined the UK's largest port owner in February 1997.
"APS is an excellent strategic acquisition for ABP which allows us to extend our port operations into North America,'' Smith said in a statement.
ABP shares were down 2p at 365p. APS shares rose 6.5p to 186p.
APS was established in 1995 as a vehicle to sell shares in the Port of Benicia in California and later expanded with the purchase of the Hobelmann Group, a port services business on the eastern seaboard of the US. APS also manages nine US airports.
The company had profits before tax of pounds 6.3m on sales of pounds 37.5m last year, compared with ABP's pre-tax profit of pounds 99m on sales of pounds 286.9m.
With 23 ports, ABP handles about one-quarter of the UK's seaborne trade. Smith has reorganised its ports operation and launched a pounds 100m share buy-back in an effort to accelerate earnings growth.