I mean all the components, such as ribosomal RNA (rRNA) are synthesized in the nucleolus, but is the whole ribosome structure assembled in the nucleolus or is it also done in the rough endoplasmic reticulum and Golgi apparatus?
Ribosome assembly starts in the nucleolus (of eukaryotes) and finishes in the cytoplasm. However, in the cytoplasm the Golgi apparatus is certainly not involved, and, as some cells have little rough endoplasmic reticulum, assembly does not require that. Thus, the abstract of a review by Fromont-Racine et al. in Gene (2003) vol 313 pp. 17–42 starts with the statement:
Ribosome synthesis is a highly complex and coordinated process that occurs not only in the nucleolus but also in the nucleoplasm and the cytoplasm of eukaryotic cells.
In the 26 pages of this review there is not a single mention of the words ‘endoplasmic reticulum’ or ‘Golgi’.
A more recent (and freely available) review by Thomson et al. in Journal of Cell Science (2013) vol 126 pp. 4815-4820 is in accord with this. It has a pretty poster insert which presents the assembly as a succession of events, starting in the nucleolus, proceeding to the nucleoplasm, and with some final polishing in the cytoplasm.