Blazars are the most extreme active galactic nuclei, having relativistic jets that are closely aligned to our line of sight. They are the most powerful persistent astrophysical sources of non-thermal electromagnetic radiation in the Universe, with spectral energy distributions (SEDs) spanning ~15 decades in energy, from radio frequencies up to high-energy γ-rays. Blazar SEDs vary both in terms of energy flux (i.e. flux variability) and spectral characteristics (i.e. color changes) on timescales ranging from minutes to years. Decade monitoring of blazars at optical and infrared (O/IR) wavelengths with the meter-class telescopes of the Small and Moderate Aperture Research Telescope System (SMARTS) in Chile and in γ-rays with the Fermi Large Area Telescope (LAT) has enabled the systematic study of multi-wavelength long-term variability in blazars. In this study we investigate, from a theoretical perspective, the long-term variability properties of blazar emission by introducing an observationally motivated time-dependence to four main parameters of the one-zone leptonic model: electron injection luminosity, magnetic field strength, Doppler factor and external photon field luminosity. For the first time, we use both the probability density function (PDF) and the power spectrum density (PSD) of the observed 10 year-long Fermi-LAT light curves to create fake γ-ray light curves and variation patterns for the model parameters in order to simulate the long-term multi-wavelength flux variability for the full time-interval of 10 years. To quantify the latter, we use standard timing tools, such as discrete correlation functions (DCFs) and fractional variabilities (FVs). Our goal is to compare the findings of our theoretical investigation with observations of two bright blazars from the SMARTS sample (PKS 2155-304 and 3C 273), and to understand the cause of the observed time lags between O/IR wavelengths and γ-rays.