The ability to express transgenes at specified levels is critical for understanding cellular behaviors, and for applications in gene and cell therapy. Transfection, viral vectors, and other gene delivery methods produce varying protein expression levels, with limited quantitative control, while targeted knock-in and stable selection are inefficient and slow. Active compensation mechanisms can improve precision, but the need for additional proteins or lack of tunability have prevented their widespread use. Here, we introduce a toolkit of compact, synthetic miRNA-based circuit modules that provide precise, tunable control of transgenes across diverse cell types. These circuits, termed DIMMERs (Dosage-Invariant miRNA-Mediated Expression Regulators) use multivalent miRNA regulatory interactions within an incoherent feed-forward loop architecture to achieve nearly uniform protein expression over more than two orders of magnitude variation in underlying gene dosages or transcription rates. They also allow coarse and fine control of expression, and are portable, functioning across diverse cell types. In addition, a heuristic miRNA design algorithm enables the creation of orthogonal circuit variants that independently control multiple genes in the same cell. These circuits allowed dramatically improved CRISPR imaging, and super-resolution imaging of EGFR receptors with transient transfections. The toolbox provided here should allow precise, tunable, dosage-invariant expression for research, gene therapy, and other biotechnology applications.