Low frequency 1/f noise is one of the key limiting factors of high precision measurement instruments. In this paper, digital correlated double sampling is implemented to reduce the offset and low frequency 1/f noise of a data acquisition system with 24-bit sigma delta (Σ-Δ) analog to digital converter (ADC). The input voltage is modulated by cross-coupled switches, which are synchronized to the sampling clock, and converted into digital signal by ADC. By using a proper switch frequency, the unwanted parasitic signal frequencies generated by the switches are avoided. The noise elimination processing is made through the principle of digital correlated double sampling, which is equivalent to a time shifted subtraction for the sampled voltage. The low frequency 1/f noise spectrum density of the data acquisition system is reduced to be flat down to the measurement frequency lower limit, which is about 0.0001 Hz in this paper. The noise spectrum density is eliminated by more than 60 dB at 0.0001 Hz, with a residual noise floor of (9 ± 2) nV/Hz(1/2) which is limited by the intrinsic white noise floor of the ADC above its corner frequency.