Contrary to popular belief, Sita was not the next birth of Brihaspati's granddaughter Vedavati. This confusion arises from an even more fundamental fact about the Ramayana that few people are familiar with: Sita was never kidnapped! That might seem shocking; in most people's understanding of the Ramayana, Ravana kidnaps Sita while Rama is lured away by Marichan in the form of a golden deer, and Rama goes to Lanka and rescues her from Ravana. But that is not actually what happened; Vishnu himself describes the actual sequence of events in this excerpt from the Venkatachala Mahatmya of the Skanda Purana:
Formerly, in the auspicious Treta Yuga, I killed Ravana. At that time the girl Vedavati rendered assistance to Sri (Sita). Lakshmi appeared in the land of Janaka in the form of Sita. In the Panchavati forest, when I went away to kill Maricha, my younger brother followed me on being urged by Sita. In the meantime the king of Rakshasas came there to abduct Sita. Fire-god present in the (place of) Agnihotra sacrifice knew (i.e. anticipated) the attempt of Ravana. He took the real Sita to Patala and entrusted her to (his wife) Svaha. There was a splendid lady named Vedavati. Formerly, she was touched by the same Rakshasa (but not molested). Yet she cast off her body in fire. In order to kill Ravana she was created once again. It was she who was abducted by Ravana and kept in custody in Lanka. Afterwards when Ravana was killed, she entered fire once again. Agni handed over Lakshmi, my Janaki, who had been kept in protective custody by Svaha and told me about the attendant accompanying Sita.
Vedavati did all this to take revenge on Ravana, for what he had attempted to do to her. So Rama crossed an ocean and fought a war to rescue Sita, when Sita was never in any actual danger.
Now why do people think that Sita was the next birth of Vedavati? It's because of the fact that the woman held in Lanka was genuinely Vedavati, since it was assumed that Sita was the woman held in Lanka, people thought that Sita and Vedavati were one and the same. For instance, in the Yuddha Kanda of the Ramayana, Ravana says "Further, I was formerly cursed by Vedavati when she was humiliated by me. The same Vedavati is born as the highly fortunate Seetha the daughter of Janaka."
Now in contrast to Sita, who was an incarnation of Vishnu's wife Lakshmi, Vedavati was an incarnation of Vishnu's other wife Bhumidevi. And after Rama was reunited with Sita, he was asked to marry Vedavati, but he refused, saying that he can only marry one woman in this birth:
On hearing the words of Fire-god, the splendid (genuine) Sita told me: "O Lord, this Vedavati has always done everything pleasing to me. Hence she is a great devotee of the Lord. Hence, O Lord, choose her (as wife)." I replied "O goddess, I shall do so in the twenty-eighth Kali Yuga. Till then let her stay in the world of Brahma and be adored by Devas."
So Vedavati was reborn in the Kali Yuga as the princess Padmavathi, daughter of Akasa Raja, and she finally married Vishnu as described in the famous story of Venkateshwara (the Vishnu deity in Tirupati, AKA Srinivasa or Balaji).