Here we present a Golden Gate assembly system adapted for the rapid genomic engineering of the industrial fungus Ashbya gossypii. This biocatalyst is an excellent biotechnological chassis for synthetic biology applications and is currently used for the industrial production of riboflavin. Other bioprocesses such as the production of folic acid, nucleosides, amino acids and biolipids have been recently reported in A. gossypii. In this work, an efficient assembly system for the expression of heterologous complex pathways has been designed. The expression platform comprises interchangeable DNA modules, which provides flexibility for the use of different loci for integration, selection markers and regulatory sequences. The functionality of the system has been applied to engineer strains able to synthesize polyunsaturated fatty acids (up to 35% of total fatty acids). The production of the industrially relevant arachidonic, eicosapentanoic and docosahexanoic acids remarks the potential of A. gossypii to produce these functional lipids.