We study current fluctuations in tunnel junctions driven by a voltage source. The voltage is applied to the tunneling element via an impedance providing an electromagnetic environment of the junction. We use circuit theory to relate the fluctuations of the current flowing in the leads of the junction with the voltage fluctuations generated by the environmental impedance and the fluctuations of the tunneling current. The spectrum of current fluctuations is found to consist of three parts: a term arising from the environmental Johnson‐Nyquist noise, a term due to the shot noise of the tunneling current and a third term describing the cross‐correlation between these two noise sources. Our phenomenological theory reproduces previous results based on the Hamiltonian model for the dynamical Coulomb blockade and provides a simple understanding of the current fluctuation spectrum in terms of circuit theory and properties of the average current. Specific results are given for a tunnel junction driven through a resonator.