Lalrinzuala was signed on loan from Indian Super League (ISL) Chennaiyin FC while Pradhan was hired from FC Pune City.
Lalrinzuala, 18, was recently named the "Emerging Player" of the ISL.
The left back has made 13 appearances for Chennaiyin and has been part of every age group of the Indian national side from the U-14 set-up to the U-19 level.
DSK coach Dave Rogers said, in a release: "I knew that this boy was going to be something special as his ability as a left back, not just defensively but offensively, is outstanding.
"His energy levels, to get up and down the pitch, along with his quality on the ball, have improved immensely; and also defensively he has grown into the best young defender in the country.
"I am delighted to have signed Jerry and have no doubt that he can reach new levels with us here at DSK Shivajians. I look forward to continuing his development on the right pathway."
Pradhan, a veteran midfielder in the country's football circuit, will add experience and impetus to the position.
"His energy and his enthusiasm fit in perfectly to the style and tempo of football we play at DSK Shivajians.
"He has great experience and a real appetite to continue progressing in his career and provides me with versatility and quality which will help our young squad."