We address the problem of reconstructing a sparse signal from compressive measurements with the aid of multiple known correlated signals. We propose a reconstruction algorithm with multiple side information signals (RAMSI), which solves an minimization problem by weighting adaptively the multiple side information signals at every iteration. In addition, we establish theoretical bounds on the number of measurements required to guarantee successful reconstruction of the sparse signal via weighted minimization. The analysis of the derived bounds reveals that weighted minimization can achieve sharper bounds and significant performance improvements compared to classical compressed sensing (CS). We evaluate experimentally the proposed RAMSI algorithm and the established bounds using numerical sparse signals. The results show that the proposed algorithm outperforms state-of-the-art algorithms—including classical CS, ℓ1-ℓ1 minimization, Modified-CS, regularized Modified-CS, and weighted ℓ1 minimization—in terms of both the theoretical bounds and the practical performance.