We present the transition of the universe from the early decelerating phase to the current accelerating phase with viscous fluid and time-dependent cosmological constant (A) as a source of matter in Bianchi- V spacetime.To study the transit behaviour of the universe,we assume the scale factor as an increasing function of time,which generates a time-dependent deceleration parameter (DP).The study revesls that the cosmological term does not change its fundamental nature for ε =const and ε =ε(t),where ε is the coefficient of bulk viscosity.The A(t)is found to be positive and is a decreasing function of time.The same behavior was observed during recent supeovae observations.The physical behaviour of the universe is discussed in detail.