We consider a system of two-parameter deformed boson oscillators whose spectrum is given by a generalized Fibonacci sequence. In order to establish the role of the deformation parameters (q(1), q(2)) in the thermostatistics of the system, we calculate several thermostatistical functions in the thermodynamical limit and investigate the low temperature behavior of the system. In this framework, we show that the thermostatistics of the (q(1), q(2))-bosons can be studied using the formalism of Fibonacci calculus which generalizes the recently proposed formalism of q-calculus. We also discuss the conditions under which the Bose-Einstein condensation would occur in the present two-parameter generalized boson gas. However, the ordinary boson gas results can be obtained by applying the limit q(1) = q(2) = 1.