Split learning is a distributed training framework that allows multiple parties to jointly train a machine learning model over vertically partitioned data (partitioned by attributes). The idea is that only intermediate computation results, rather than private features and labels, are shared between parties so that raw training data remains private. Nevertheless, recent works showed that the plaintext implementation of split learning suffers from severe privacy risks that a semi-honest adversary can easily reconstruct labels. In this work, we propose \textsf{TPSL} (Transcript Private Split Learning), a generic gradient perturbation based split learning framework that provides provable differential privacy guarantee. Differential privacy is enforced on not only the model weights, but also the communicated messages in the distributed computation setting. Our experiments on large-scale real-world datasets demonstrate the robustness and effectiveness of \textsf{TPSL} against label leakage attacks. We also find that \textsf{TPSL} have a better utility-privacy trade-off than baselines.