Noise measurements have been performed in MgO-based tunnel junctions with normalized resistance in the range of 105 - 107 Ω μ m2 and various magnetoresistance ratios were investigated. Noise measurements in the frequency range of 1-1000 Hz shows magnetically dependent pure 1f power spectra at low frequency. The 1f noise scales with bias voltage, indicating that the 1f noise can be attributed to magnetic tunnel junction resistance fluctuations. Bias voltage dependence of random telegraph noise (RTN) was observed, indicating electronic origin due to the charge-trapping mechanism. In the presence of the easy-axis bias field, our data exhibit a magnetic-field dependence of RTN that originates from magnetization fluctuations. A phenomenological noise parameter, defined for the comparison of noise levels in different junctions, was shown to be independent of the junction resistance-area product in the range investigated. This observation suggests that the decrease in tunnel resistance does not play an important role in reducing 1f noise.