A silicon-based digitally tunable positive/negative dispersion controller (DC) is proposed and realized for the first time using the cascaded bidirectional chirped multimode waveguide gratings (CMWGs), achieving positive and negative dispersion by switching the light propagation direction. A 1 × 2 Mach–Zehnder switch (MZS) and a 2 × 1 MZS are placed before and after to route the light path for realizing positive/negative switching. The device has Q stages of identical bidirectional CMWGs with a binary sequence. Thus the digital tuning is convenient and scalable, and the total dispersion accumulated by all the stages can be tuned digitally from - ( 2^Q - 1 ) D₀ to ( 2^Q - 1 ) D₀ with a step of D₀ by controlling the switching states of all 2 × 2 MZSs, where D₀ is the dispersion provided by a single bidirectional CMWG unit. Finally, a digitally tunable positive/negative DC with Q = 4 is designed and fabricated. These CMWGs are designed with a 4-mm-long grating section, enabling the dispersion D₀ of about 4.16 ps / nm in a 20-nm-wide bandwidth. The dispersion is tuned from -61.53 to 63.77 ps / nm by switching all MZSs appropriately, and the corresponding group delay is varied from -1021 to 1037 ps.