Transcription is an episodic process characterized by probabilistic bursts, but how the transcriptional noise from these bursts is modulated by cellular physiology remains unclear. Using simulations and single-molecule RNA counting, we examined how cellular processes influence cell-to-cell variability (noise). The results show that RNA noise is higher in the cytoplasm than the nucleus in ∼85% of genes across diverse promoters, genomic loci, and cell types (human and mouse). Measurements show further amplification of RNA noise in the cytoplasm, fitting a model of biphasic mRNA conversion between translation- and degradation-competent states. This multi-state translation-degradation of mRNA also causes substantial noise amplification in protein levels, ultimately accounting for ∼74% of intrinsic protein variability in cell populations. Overall, the results demonstrate how noise from transcriptional bursts is intrinsically amplified by mRNA processing, leading to a large super-Poissonian variability in protein levels.