We study the cosmic evolution in radiation and matter dominated epochs of the universe in chameleon Brans-Dicke (BD) as well as generalized chameleon BD cosmology. For this purpose, we consider Bianchi I universe model with matter contents as perfect fluid and the power law ansatz for scale factors, scalar field, interacting function f(phi), chameleon potential V (phi) and the BD parameter omega(phi). Using constraints on the involved parameters, it is shown that only the decelerated expansion of the universe can be discussed for these eras which is consistent with the astronomical observations. The graphical behavior of these functions for large values of the BD parameter (as suggested by local gravity tests) are also given. Finally, we evaluate statefinders as well as cosmological distances for obtained models.