Jovanovic agreed a Bosman deal with Liverpool in February, when Benitez was still in charge at Anfield, and he insists the Spaniard's departure from the club will no have bearing on his switch to Merseyside.
The 29-year-old insists he will link up with his new team-mates next month once he receives his work permit.
"I am going to Liverpool. I have signed there for three years. I repeat: no pre-agreement - a real contract," Jovanovic told Nieuwsblad.
"And the departure of Benítez changes nothing. I have maintained contact with the executive board of Liverpool and everything is good.
"I am working to arrange my visa for England. Next week I go there to collect my work permit.
"Everything is in order since in the last two years I have played 75 per cent of the matches for my national side. Next I am looking for a house.
"On the 14th or 15th July I will join the squad for a training camp in Switzerland. But, as from Thursday, I want to start my individual training programme so I can show them immediately that I am worth a place in the side."