The 32-year-old offspin-bowling allrounder has played six Tests, taking 16 wickets at an average of 29.06 and scoring 248 runs at 31.00, including a century against England in Mumbai. He last featured for India in the Mohali Test against Sri Lanka earlier this year.
Warwickshire are currently placed eighth among ten teams in Division One and need a strong finish to climb above the bottom two and avoid being relegated to Division Two.
Jayant will be the eighth Indian player to feature in English domestic cricket this year, and the third signed by Warwickshire, after Siraj and Krunal Pandya, who played five Royal London One-Day Cup matches before a groin injury ended his stint.
The others are Cheteshwar Pujara (Sussex), Washington Sundar (Lancashire), Umesh Yadav (Middlesex), Navdeep Saini (Kent) and Shubman Gill (Glamorgan).
"This will be my first County Championship experience and I'm incredibly excited to join up with the squad for the final three games," Jayant said. "When I was asked if I would like to join Warwickshire it was something I couldn't say no to. Having played my sixth Test earlier this year, I believe these three games will help me improve my game for more opportunities in the near future.
"I have never played at Edgbaston, but I have heard great things about the stadium and it will be a privilege to call it my home."
Paul Farbrace, Warwickshire's director of cricket, hoped Jayant's signing would help the team stay up. "Jayant is another fantastic addition to the squad, and we're excited to welcome him to Warwickshire," he said. "Jayant has played Test cricket this year and adding his First-Class experience to our bowling attack could be vital in the final three games.
"It was vitally important that we strengthened our bowling line-up for the run-in and the signing of Jayant, plus Siraj gives us an enviable array of options."