This paper investigates the time-varying formation tracking (TVFT) control problem considering a constant input delay and unknown external disturbances for the general linear multi-agent system (MAS) under a directed communication graph containing a spanning tree. To achieve that, a new time-varying shape format is firstly proposed. Then, a disturbance observer (DO) is introduced to compensate the unknown disturbance effect. After that, the Artstein's model reduction technique is adopted and modified to design a state predictor in order to transform the MAS with a delayed input into a delay-free system. Fourthly, an adaptive observer (AO), which is used to estimate the designed state predictor, is proposed by using the neighbors’ information such as the inputs, time-varying shapes, DOs, AOs and relative state measurements. The convergence of closed-loop system is guaranteed by the designed algebraic Riccati equation. The whole controller requires no eigenvalue information of the Laplacian matrix of communication graph, thus is fully distributed. Finally, the effectiveness of proposed fully distributed controller (FDC) is verified by numerical examples and factors influencing FDC performances are analyzed.