The proposals provoked protests from parents, teachers and writers for two years, and the court ruling is the culmination of a long legal battle by opponents of the spelling reform.
The case was brought by the parents of nine-year-old twins who wanted to prevent their children learning the new spelling.
The court ruled against the plaintiffs who had argued that the reforms could only be approved by an act of parliament.
There have been many court cases at lower levels, and confusion with some federal states approving the reforms and some ruling against.
The constitutional court ruling is now expected to end the legal battles and smooth the way for the introduction of the new spellings at the beginning of August.
Advocates of the reform argue it will make a complex language much easier to learn.
The new rules iron out some of the anomalies that have made German a difficult language for even the most competent linguist.
There will be substantial changes to the use of the umlaut in words with long 'e' sounds and changes to the use of the diphthong - the 'oy' sound.
The German-language symbol for the double 's' - ß - is being retained in most circumstances but the fiendishly complex rules concerning the correct placement of commas will be seeing a number of changes.
Opponents of the spelling reform say it is unnecessary and confusing and will deprive German of some of its linguistic subtlety.
Most German schoolchildren already learn the new spellings, and publishers have spent millions of dollars adapting school textbooks and dictionaries.
Publishers and printers had warned of financial ruin if the reforms were overturned.
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