Satyavati was the daughter of Chediraj Vasu and she was brought up by Nishadraj. When Shantanu felt a very pleasant and strong smell in a jungle near bank of Yamuna river, he saw Satyavati and immediately fell in love. She introduced herself as Nishad Kanya and her father as Nishadraj. Shantanu went to Nishadraj and asked for her hand in marriage. Nishadraj said that he would only marry off his daughter to him if he promised that her son would inherit the throne. Even being extremely attracted and in love with Satyavati, he didn't promise him anything and returned to Hastinapur. But Shantanu became very sad and pale due to love sickness.
When Prince Devvrata (son of Ganga) asked his father about his growing sadness and grief, he lied that he only had one son and he wanted more sons for the continuation of the line otherwise he didn't wanna marry again. He said that Devvrata is equal to many sons but he still wanted more children as he saw him always indulging and practicing warship. Not convinced with this answer he first enquired his minister and then his chariot. He told him that Shantanu was lovesick for Nisharaj’s daughter but he rejected the proposal.
Then Bhishma with ministers went to Nisharaj and asked for her hand for his father. He promised Nishadraj that he would not take the throne and Satyavati’s son would be the next King. But Nisharaj wanting more assurance denied the proposal saying that Devvrat’s sons would not accept this and want their right. Then Devvrat did something really unthinkable, he took oath to never marry in his life or have any children or even indulge in any physical and intimate pleasures. He vowed to be extreme celibrate. This caused goosebumps to Nisharaj and then convinced he accepted to give Satyavati to Shantanu. Hearing this terrible oath, people started calling him Bhishma. Shantanu shocked but extremely happy gave boon to his son to not die till Bhishma himself wanted it.
Satyavati became mother of Chitrangada and Vichitravirya. She had a son named Vyas Muni with Rishi Parashar before her marriage with Shantanu.
Source: Mahabharata