We identify 85 variable galaxies in the GOODS North and South fields using 5 epochs of HST ACS V-band (F606W) images spanning 6 months. The variables are identified through significant flux changes in the galaxys nucleus and represent ~2% of the survey galaxies. With the aim of studying the active galaxy population in the GOODS fields, we compare the variability-selected sample with X-ray and mid-IR AGN candidates. Forty-nine percent of the variables are associated with X-ray sources identified in the 2Ms Chandra surveys. Twenty-four percent of X-ray sources likely to be AGN are optical variables and this percentage increases with decreasing hardness ratio of the X-ray emission. Stacking of the non-X-ray detected variables reveals marginally significant soft X-ray emission. Forty-eight percent of mid-IR power-law sources are optical variables, all but one of which are also X-ray detected. Thus, about half of the optical variables are associated with either X-ray or mid-IR power-law emission. The slope of the power-law fit through the Spitzer IRAC bands indicates that two-thirds of the variables have BLAGN-like SEDs. Among those galaxies spectroscopically identified as AGN, we observe variability in 74% of broad-line AGNs and 15% of NLAGNs. The variables are found in galaxies extending to z~3.6. We compare the variable galaxy colors and magnitudes to the X-ray and mid-IR sample and find that the non-X-ray detected variable hosts extend to bluer colors and fainter intrinsic magnitudes. The variable AGN candidates have Eddington ratios similar to those of X-ray selected AGN.
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