Monday's unanimous decision by the three-judge panel targeted the Florida-based Eller Company.
P&O acknowledged the appeal ruling and said its sale to DP World would now proceed.
Eller Company had gone to London's High Court last week to block the takeover, arguing that the transaction would flout a joint venture deal it had with a subsidiary of P&O in the port of Miami.
But the High Court last Thursday approved the takeover of the Peninsula and Oriental Steam Navigation Company (P&O) by DP World, prompting a move by Eller to appeal.
The planned $6.9-billion transaction has sparked bitter controversy in the United States, where critics fear that allowing DP World, controlled by the Dubai government, to assume the management of six P&O-administered US ports could compromise security.
While sparking intense opposition in Congress, the deal had the backing of George Bush, the US resident, as well as other senior administration officials.
In a bid to calm the storm, DP World agreed last week to postpone finalising the transaction to allow for a 45-day review by US authorities.
DP World has said it will not intervene in P&O's US operations before May.
Although some lawmakers are moving to author legislation that would torpedo the takeover, Bush has said he would veto it.
The sale of P&O brings an end to the independence of the 169-year-old company established during the reign of Queen Victoria.
The transaction will create the second-biggest global ports and container group in terms of traffic, on par with Singapore's PSA International and the Danish group APM Terminals.
Hutchinson Ports of Hong Kong is number one worldwide.