Long Period Variable stars are ubiquitous among the bright red giant branch stars in NGC 5128. Mostly they are found to be brighter than the tip of the first ascent giant branch with magnitudes ranging from about $K=19$ to $K=21.5$. They have periods between 155 and 1000 days and K-band amplitudes between 0.1 and 2 mag, characteristic of semi-regular and Mira variables. We compare the colors, periods and amplitudes of these variables with those found in old stellar populations like Galactic globular clusters and Galactic bulge as well as with intermediate-age Magellanic Cloud long period variables. The population of stars above the tip of the red giant branch (RGB) amounts to 2176 stars in the outer halo field (Field 1) and 6072 stars in the inner halo field (Field 2). The comparison of the luminosity functions of the Galactic bulge, M 31 bulge and NGC 5128 halo fields shows an excess of bright AGB stars extending to $M_K\simeq -8.65$. The large majority of these sources belong to the asymptotic giant branch (AGB) population in NGC 5128. Subtracting the foreground Galactic stars and probable blends, at least 26% and 70% of AGB stars are variable in Fields 1 and 2, respectively. The average period of NGC 5128 LPVs is 395 days and the average amplitude 0.77 mag. Many more short period Miras are present in Field 2 than in Field 1 indicating a difference in the stellar populations between the two fields. Period and amplitude distributions and near-IR colors of the majority of LPVs in NGC 5128 are similar to the Galactic bulge variables. However, some ~10% of LPVs have periods longer than 500 days and thus probably more massive, hence younger, progenitor stars. A few carbon star candidates are identified based on their red $J-H$ and $H-K$ colors.