Tyagi has two daughters from his first marriage.[3] He met actress Rakshanda Khan in 2006, on the set of the show Kuch Apne Kuch Paraye.[4] They dated for seven years and got married in 2014.[5][6] Khan gave birth to their daughter in December 2014.[7]
In August 2020, Tyagi tested positive for COVID-19,[8][9] but he recovered by September.[10][11]
Tyagi came to Mumbai in 1993, initially working as a car trader; he aspired to become a singer.[12] He launched an album in 2003, which according to him "did fairly well".[2] He subsequently ventured into acting in television shows, beginning with Family Business and Tumhari Disha (both 2004).[2][13] Trained in classical music by maestro Upendra Verma, he won the singing reality show Jjhoom India in 2007, alongside his partner Madhushree, beating Varun Badola.[2][13]
Tyagi gained prominence with his portrayal of Manish Goenka in Rajan Shahi's TV series Yeh Rishta Kya Kehlata Hai. Tyagi has been playing Manish Goenka since 2016, making his role span 3 generations of the longest-running daily soap of India.[17] He plays Kartik Goenka's father, Akshara Sharma's grandfather and Abhira Poddar's great-grandfather in the series.[18]