Here are some possible correct ways to express this sentiment:
More direct translations:
* Me alegro de ser tuyo/tuya. (I'm glad to be yours.)
* Estoy feliz de ser tuyo/tuya. (I'm happy to be yours.)
More nuanced expressions:
* Me alegra mucho estar contigo. (I'm very happy to be with you.)
* Soy muy feliz de tenerte en mi vida. (I'm very happy to have you in my life.)
The best choice depends on the specific context and the level of formality you want to express.