The Serbia forward is expected to make his competitive debut for the Reds in Thursday night's Europa League qualifier against FK Rabotnicki.
The 29-year-old, who can play on the left wing or as a striker, was lured to Merseyside by former boss Rafa Benitez on a free transfer.
And former Standard Liege attacker Jovanovic revealed how he had previously rejected a move to the Bernabeu after he was not guaranteed regular first-team football.
"I think 99 per cent of people I spoke to told me they did not understand why I said no to Real," said Jovanovic, who scored Serbia's winner against Germany in the group stage of the World Cup.
"But maybe I am special. I thought if I went it would be as an ordinary player, but that, if I stayed, I would be where I felt good, where I was a star in Belgium.
"It is only a small league but Standard Liege won two titles and two Super Cups while I was there and I won two personal awards, one from coaches and players and the second from journalists. So I was very happy.
"Real offered me just a one-year deal with an option for two years. I said four, they said no and so I turned them down. Maybe they are the biggest club in the world, but I always knew that other big clubs would come.
"I will never go somewhere where I only play a small part. Why? It is better to be happy somewhere. Now I only want to look forward and play for Liverpool."