Compost application may be an effective means to rapidly increase soil organic matter, soil quality, and soil microbial community diversity in intensive potato crop production systems. This study compared three contrasting compost products with a no compost control on soil chemical properties and soil bacterial and fungal community composition and diversity. The three composts consisted of municipal source separate waste compost (SSOC), forestry and poultry manure compost (FPMC), and forestry residues waste compost (FRC) with low, medium and high forestry waste percentages in their feedstock, respectively. Soil samples were collected on four dates over 11 months after compost application in October 2014. Soil pH, dissolved organic carbon and readily mineralizable C (respiration) were significantly greater in FPMC- and SSOC-treated soils compared to FRC-treated and control soils. Compost application influenced the relative abundances of several bacterial phyla in soils compared to control soils but not the relative abundances of fungal phyla. Several compost-borne bacterial (average of 383 operational taxonomic units (OTUs)) and fungal (average of 66 OTUs) species could be detected in soil throughout the following growing season after compost product application suggesting that these species succeeded in establishing in soils. The β-diversity of bacterial and fungal communities in soils differed significantly among treatments and sampling dates, indicating that the applied composts resulted in a change in the bacterial and fungal community diversity. Convergence of bacterial community diversity was observed among treatments over time but not for fungal community. The application of diverse compost products clearly changed the soil chemical properties which in turn influenced the bacterial and fungal communities. The effects of compost application on microbial communities were persistent, and could still be observed nearly a year after compost was applied.