Hardware (HW) security issues have been emerging at an alarming rate in recent years. Transient execution attacks, in particular, pose a genuine threat to the security of modern computing systems. Despite recent advances, understanding the intricate implications of microarchitectural design decisions on processor security remains a great challenge and has caused a number of update cycles in the past. number of update cycles in the past. This papers addresses the need for a new approach to HW sign-off verification which guarantees the security of processors at the Register Transfer Level (RTL). To this end, we introduce a formal definition of security with respect to transient execution attacks, formulated as a HW property. We present a formal proof methodology based on Unique Program Execution Checking (UPEC) which can be used to systematically detect all vulnerabilities to transient execution attacks in RTL designs. UPEC does not exploit any a priori knowledge on known attacks and can therefore detect also vulnerabilities based on new, so far unknown, types of channels. This is demonstrated by two new attack scenarios discovered in our experiments with UPEC. UPEC scales to a wide range of HW designs, including in-order processors (RocketChip), pipelines with out-of-order writeback (Ariane), and processors with deep out-of-order speculative execution (BOOM). To the best of our knowledge, UPEC is the first RTL verification technique that exhaustively covers transient execution side channels in processors of realistic complexity.