The scrip gained 4.77 per cent to settle at Rs 907.25 on BSE. During the day, it jumped 9.52 per cent to Rs 948.45.
On NSE, shares of the company went up by 5 per cent to end at Rs 908.70.
Tata Sons will hold the remaining 49 per cent stake in the company, Quess said in a filing to BSE yesterday.
Quess Corp Chairman and MD Ajit Isaac said: "We are excited about our partnership with the Tata Group. This investment marks a significant milestone for Quess in its journey to build a world class business services platform."
TBSS is among India's premier customer experience management companies, with over 10 years of sectoral expertise, Quess Corp said.