We propose and numerically demonstrate two novel terahertz absorbers made up of periodic single- and double-layer decussate graphene ribbon arrays. The simulated results show that the proposed absorbers have narrowband near-unity terahertz absorption with ultra-wide frequency reconfiguration and angular stability. By tuning the Fermi level of graphene ribbons, the over 90% absorbance peak frequency of the absorber with single-layer graphene structure can be flexibly adjusted from 6.85 to 9.85 THz for both the transverse magnetic (TM) and transverse electric (TE) polarizations. This absorber with single-layer graphene demonstrates excellent angular stability with the absorbance peaks of the reconfigurable absorption bands remaining over 99.8% in a wide angle of incidence ranging from 0 to 70°. The tuning frequency can be significantly enhanced by using the absorber with double-layer graphene structure from 5.50 to 11.28 THz and 5.62 to 10.65 THz, approaching two octaves under TM and TE polarizations, respectively. The absorbance peaks of the reconfigurable absorption band of this absorber for both polarizations maintain over 70%, even at a large angle of incidence up to 70°. Furthermore, an analytical fitting model is also proposed to accurately predict the absorbance peak frequencies for this variety of absorbers. Benefitting from these attractive properties, the proposed absorber may have great potential applications in tunable terahertz trapping, detecting, sensing, and various terahertz optoelectronic devices.