A computationally-efficient algorithm for blind Doppler frequency estimation from orthogonal frequency division multiplexing (OFDM) signals is proposed. The objective of this algorithm is to estimate the Doppler frequency of received low Earth orbit (LEO) satellite OFDM signals, which are planned for massive future deployment. A method for resolving the ambiguity in the resulting Doppler estimate is discussed. To demonstrate the efficacy of the proposed algorithm, and knowing that the considered LEO satellite constellations are not fully deployed yet, experiments are conducted with real terrestrial fifth-generation (5G) New Radio (NR) signals. The experimental results show a ground vehicle traversing a 6.5 km trajectory in 700 seconds, while blindly estimating the Doppler frequency of received 5G signals, achieving a Doppler root mean squared-error (RMSE) of 6.45 Hz.