This work explores the use of Ge-rich graded-index Si_1-xGex rib waveguides as building blocks to develop integrated nonlinear optical devices for broadband operation in the mid-IR. The vertical Ge gradient concentration in the waveguide core renders unique properties to the guided optical mode, providing tight mode confinement over a broadband mid-IR wavelength range from λ = 3 µm to 8 µm. Additionally, the gradual vertical confinement pulls the optical mode upwards in the waveguide core, overlapping with the Ge-rich area where the nonlinear refractive index is larger. Moreover, the Ge-rich graded-index Si_1-xGex waveguides allow efficient tailoring of the chromatic dispersion curves, achieving flat anomalous dispersion for the quasi-TM optical mode with D ≤ 14 ps/nm/km over a ~1.4 octave span while retaining an optimum third-order nonlinear parameter, γeff. These results confirm the potential of Ge-rich graded-index Si_1-xGex waveguides as an attractive platform to develop mid-IR nonlinear approaches requiring broadband dispersion engineering.