The decision has been expected as the St Vitus Metropolitan Chapter withdrew its complaint in June following an agreement between the state and the church.
The US judges then waited for a month whether another church body would withdraw its complaint over the ownership of the All Saints Church at Prague Castle, which did not happen.
The dispute between the state and the church over the cathedral, which was founded in the 14th century and fully completed in 1929, has lasted since 1992.
Under the latest court verdict, the cathedral belongs to the state. The Metropolitan Chapter lodged a constitutional complaint against the verdict in May 2009.
The previous court verdicts ascribed the cathedral's ownership to the church, but the state appealed and the Supreme Court (NS) cancelled the decision.
In the new proceedings the lower-level courts definitively decided that the cathedral's owner is the state. The NS upheld the decision.
The NS based its position on the government directive from 1954 that declared Prague Castle as a protected heritage area belonging to the Czechoslovak people, that is to the state.
The agreement on joint care of the cathedral was signed in May by President Vaclav Klaus and new Prague Archbishop Dominik Duka.
It says the court disputes about the cathedral will not continue, and that the dispute should be solved on the basis of a mutual consensus.
Prague Castle is the seat of the Presidential Office.
St Vitus Cathedral is the most visited Czech church and a symbol of Czech statehood.
In the past, Czech kings were crowned in it, and the remains of significant Czech sovereigns, noblemen and church dignitaries are buried in the cathedral.
Czech coronation jewels are also kept in the cathedral.
SIC: PDM