Multi-Spectral Fluorescent Lifetime Imaging Microscopy (m-FLIM) is a technique that aims to perform noninvasive in situ clinical diagnosis of several diseases. It measures the endogenous fluorescence of molecules, recording their lifetime decay in different wavelength bands. This signal is a mixed response of multiple fluorescent components present in a tissue sample. The goal is to decompose the mixture and estimate the proportional contributions of its constituents. Estimation of such quantitative description will help to characterize the molecular constitution of a given sample. This paper presents a new method to estimate the abundances of multiple components present in a mixture measured using m-FLIM data. It provides a closed-form solution under the fully constrained linear unmixing model and assuming the number of components as well as their ideal lifetime decays are known. Its performance is tested using synthetic samples with three components, where performance can be measured accurately and the percentage error is around 6%. The algorithm was also validated performing unmixing of ex vivo data samples from atherosclerotic human tissue containing collagen, elastin and low-density lipoproteins. These experiments were validated against ground-truth maps, which only give a quantitative description, and the estimated accuracy was around 88%.