We propose a novel description-based controllable text-to-speech (TTS) method with cross-lingual control capability. To address the lack of audio-description paired data in the target language, we combine a TTS model trained on the target language with a description control model trained on another language, which maps input text descriptions to the conditional features of the TTS model. These two models share disentangled timbre and style representations based on self-supervised learning (SSL), allowing for disentangled voice control, such as controlling speaking styles while retaining the original timbre. Furthermore, because the SSL-based timbre and style representations are language-agnostic, combining the TTS and description control models while sharing the same embedding space effectively enables cross-lingual control of voice characteristics. Experiments on English and Japanese TTS demonstrate that our method achieves high naturalness and controllability for both languages, even though no Japanese audio-description pairs are used.