Yoga is not a religion. It is a philosophy that began in India an estimated 5,000 years ago. The father of classical ashtanga yoga (the eight-limbed path, not to be confused with Sri K. Pattabhi Jois’ Ashtanga yoga) is said to be Patanjali, who wrote the Yoga Sutra. These scriptures provide a framework for spiritual growth and mastery over the physical and mental body. Yoga sometimes interweaves other philosophies such as Hinduism or Buddhism, but it is not necessary to study those paths in order to practice or study yoga.
It is also not necessary to surrender your own religious beliefs to practice yoga.