Gene duplications play a key role in the emergence of novel traits and in adaptation. But despite their centrality to evolutionary processes, it is still largely unknown how new gene duplicates are initially fixed within populations and later maintained in genomes. Long-standing debates on the evolution of gene duplications could be settled by determining the relative importance of genetic drift vs. positive selection in the fixation of new gene duplicates. Using the Drosophila Global Diversity Lines (GDL), we have combined genome-wide SNP polymorphism data with a novel set of copy number variant calls and gene expression profiles to characterize the polymorphic phase of new genes. We found that approximately half of the roughly 500 new complete gene duplications segregating in the GDL lead to significant increases in the expression levels of the duplicated genes and that these duplications are more likely to be found at lower frequencies, suggesting a negative impact on fitness. However, we also found that six of the nine gene duplications that are fixed or close to fixation in at least one of the five populations in our study show signs of being under positive selection, and that these duplications are likely beneficial because of dosage effects, with a possible role for additional mutations in two duplications. Our work suggests that in Drosophila, theoretical models that posit that gene duplications are immediately beneficial and fixed by positive selection are most relevant to explain the long-term evolution of gene duplications in this species.