The main aim of this paper is an extension of the cosmological model with variable gravitational constant G and cosmological constant Λ which has been developed within the framework of f(R,T)) gravity. The study is motivated by earlier investigations of anisotropic Bianchi Type I cosmological models with varying G and Λ in General Relativity. The present work generalizes these models by considering a homogeneous Bianchi Type I space-time filled with a perfect fluid and incorporating variable G and Λ in modified gravity. The analysis focuses on the specific form f(R,T)=R+2f(T)) where the dependence on the trace of the energy-momentum tensor introduces modifications to Einstein’s field equations. Exact solutions of the modified field equations have been obtained for an anisotropic Bianchi Type I universe with a time-dependent cosmological term. The model naturally describes both the early inflationary phase and the present accelerated expansion of the universe, providing a unified cosmological scenario. The physical and geometrical behavior of the model has been examined through various cosmological parameters. The solutions reveal a coupling among the shear scalar σ² gravitational constant G, cosmological constant Λ and Hubble parameter H, leading to a linear relationship between these quantities. The cosmological term is assumed to vary as Λ ∝ R⁻² where R is the scale factor. The obtained model exhibits a point-type singularity at the initial epoch. At this stage, the cosmological constant becomes infinitely large, while the gravitational constant decreases with cosmic evolution. As time progresses, Λ gradually decreases, consistent with current cosmological observations. No specific equation of state or predefined functional form of G has been imposed in the analysis. Furthermore, the anisotropy decreases with time, and the universe evolves toward isotropy at late times, satisfying the condition σ → 0. Therefore, the model successfully describes a quasi-isotropic universe and provides a viable framework for studying cosmological evolution in modified f(R,T)) gravity with variable gravitational and cosmological parameters.