Elucidating regulatory effects of Alzheimer's disease (AD)-associated genetic variants is critical for unraveling their causal pathways and understanding the pathology. However, their cell-type-specific regulatory mechanisms in the brain remain largely unclear. Here, we conducted an analysis of allele-specific expression quantitative trait loci (aseQTLs) for 33 AD-associated variants in four brain regions and seven cell types using ~3000 bulk RNA-seq samples and >0.25 million single nuclei. We develop a flexible framework using a hierarchical Poisson mixed model unifying samples in both allelic and genotype-level expression data. We identified 24 AD-associated variants (~73%) that are allele-specific eQTLs (aseQTLs) in at least one brain region. Multiple aseQTLs are region-dependent or exon-specific, such as rs2093760 with CR1, rs7982 with CLU, and rs3865444 with CD33. Notably, the APOE e4 variant reduces APOE expression across all regions, even in healthy controls. In pinpointing the cell types responsible for the observed region-level aseQTLs, we found rs2093760 as an aseQTL of CR1 in oligodendrocytes but not in microglia. Many AD-associated variants are aseQTLs in microglia or monocytes of immune-related genes, including HLA-DQB1, HLA-DQA2, CD33, FCER1G, MS4A6A, SPI1, and BIN1, highlighting the regulatory role of AD-associated variants in the immune response. These findings provide further insights into potential causal pathways and cell types mediating the effects of the AD-associated variants.