Design of large‐aperture broadband arrays and array stacking of waveforms for receiver function studies critically depend on the coherence of waveforms across an array. The coherence of teleseismic P and S waves in the 0.05–1.6 Hz frequency band has been examined using high signal‐to‐noise teleseisms recorded by the USArray Transportable Array. Instrument‐corrected, time‐windowed, and rotated P and S waves were filtered in five, single‐octave frequency bands and then correlated to determine coherence in each band. The normalized correlation coefficient is used as a measure of relative coherence and plotted as a function of interstation distance, which is used as a proxy for horizontal wavelength. Up to ∼100,000 unique station correlation pairs can be found for vertical component P and transverse component S. Coherence of teleseismic P waves across the USArray is seen to be uniformly high in the frequency band between 0.05 and 0.4 Hz, with average correlation coefficients of 0.8 or greater for over 10 horizontal wavelengths. P‐wave coherence degrades at higher frequency, although coherence is still higher than 0.6 for lower mantle propagation paths. S‐wave coherence is relatively less robust but is greater than 0.8 for the 0.05–0.2 Hz frequency band, again for lower mantle propagation paths. Average coherence drops for both P and S waves for frequency bands greater than 0.2 Hz at station distances influenced by wave propagation through the upper mantle. This characteristic of wave propagation in the Earth can be used to design high‐resolution broadband phased arrays for detailed studies of large earthquake sources and Earth structure and increases confidence in using vertical stacks of P waves as effective source functions in regional receiver function analysis.