Inspired by Well-initialized Lottery Ticket Hypothesis (WLTH), which provides suboptimal fine-tuning solutions, we propose a novel fully fine-tuned continual learning (CL) method referred to as Soft-TransFormers (Soft-TF). Soft-TF sequentially learns and selects an optimal soft-network or subnetwork for each task. During sequential training in CL, Soft-TF jointly optimizes the weights of sparse layers to obtain task-adaptive soft (real-valued) networks or subnetworks (binary masks), while keeping the well-pre-trained layer parameters frozen. In inference, the identified task-adaptive network of Soft-TF masks the parameters of the pre-trained network, mapping to an optimal solution for each task and minimizing Catastrophic Forgetting (CF) - the soft-masking preserves the knowledge of the pre-trained network. Extensive experiments on Vision Transformer (ViT) and CLIP demonstrate the effectiveness of Soft-TF, achieving state-of-the-art performance across various CL scenarios, including Class-Incremental Learning (CIL) and Task-Incremental Learning (TIL), supported by convergence theory.