Intelligent reflecting surfaces (IRS), a new paradigm for controlling the wireless propagation environment, is an excellent cost-effective technology for terahertz (THz) systems. In this paper, the performance of an IRS-assisted THz system, with N reflective elements, is systematically analyzed over the deterministic IRS channel gain, the THz path loss model, and the sum of independent and non-identically distributed (i.ni.d.) cascaded alpha-mu fading channels. The probability density function (PDF) and the cumulative distribution function (CDF) of the proposed system are statistically characterized in terms of programmable multi-variate Fox's H function. Using derived statistical results, the closed-form solution for outage probability of THz-IRS system is reported along with its simple asymptotic expansions. The analytical results are validated using Monte-Carlo simulations. Results show that, sufficient signal-to-noise ratio (SNR) can be achieved with enough number of IRS antenna elements, making THz communication feasible.