Overcoming the link blockage challenges is essential for enhancing the reliability and latency of millimeter-wave (mmWave) and sub-terahertz (sub-THz) communication networks. Previous approaches relied mainly on either (i) multiple-connectivity, which under-utilizes the network resources, or on (ii) the use of out-of-band and non-RF sensors to predict link blockages, which is associated with increased cost and system complexity. In this paper, we propose a novel solution that relies only on in-band mmWave wireless measurements to proactively predict future dynamic line of sight (LOS) link blockages. The proposed solution utilizes deep neural networks and special patterns of received signal power, that we call pre-blockage wireless signatures to infer future blockages. Specifically, the developed machine learning models attempt to predict: (i) If a future blockage will occur? (ii) When will this blockage happen? (iii) What is the type of blockage? And (iv) what is the direction of the moving blockage? To evaluate our proposed approach, we build a large-scale real-world dataset comprising nearly 0.5 million data points (mmWave measurements) for both indoor and outdoor blockage scenarios. The results, using this dataset, show that the proposed approach can successfully predict the occurrence of future dynamic blockages with more than 85% accuracy. Further, for the outdoor scenario with highly-mobile vehicular blockages, the proposed model can predict the exact time of the future blockage with less than 100 ms error for blockages happening within the future 600 ms. These results, among others, highlight the promising gains of the proposed proactive blockage prediction solution which could potentially enhance the reliability and latency of future wireless networks.