The 21-year-old, accompanied by his agent Zoran Stojadinovic, travelled to the south coast of Wales on Wednesday to complete the formalities of his temporary switch.
The decision on his destination was made in a meeting on Merseyside the previous day, with Huddersfield Town also holding an interest in acquiring his services.
The Championship outfit are third in the league standings and Grujic is not only targeting promotion with his new club - who will assume his full wages - but is intent on doing enough to force his way into Jurgen Klopp’s first-team plans.
Grujic, who will wear No. 24, is hoping regular game time with the Bluebirds will help his future at Anfield.
"This is perhaps the breakthrough moment of my career,” he told MOZZART. “I am aware that I have got a great chance, playing for the next six months in a big club, and thanking Mr. Klopp for everything he has done for me."
“He encouraged me many times over the past 18 months, and I believe that I will justify his confidence. Of course, I hope I will help Cardiff gain promotion to the Premier League.”
Huddersfield had made a push for Grujic, but all parties came to the conclusion that the player would have more opportunities under Neil Warnock.
“We jointly agreed that Cardiff is the best solution,” Stojadinovic revealed. “The club is fighting to be in the Premier League, believing that Grujic is what they lack.”
Grujic is hoping to make his debut for the club away to Sheffield Wednesday on Saturday.