The Croatian international is hoping to improve the Toffees' potency in front of goal and believes he can adapt to playing in England after two years in the SPL where he scored 30 goals in 45 league games.
When asked about his aims, Jelavic told reporters: "Goals, goals and more goals. I know Everton have not scored much this season but I don't feel the pressure, I like a challenge.
"I will do my best to score many goals. I am always looking to be better every day and my ambitions are to play well and to be useful for the team and score as many goals as possible.
"I know it is a big difference but I think in Scotland you also have to be 100% and they also have tough games.
“Playing in Scotland helped me a lot and I think I am ready. The Premier League is something on a higher level and I hope it will be good for me. I don't think I will need time to settle."
The 26-year-old also revealed he offered to stay with Rangers but, due to their perilous financial situation, the club were forced to sell him.
He added: "It is a difficult situation for them, I know, and I heard inside information about them having problems.
"I spoke with [the Rangers manager] Ally McCoist and said if the president wants me to stay I'll stay and if they need money and want me to leave I'll leave – the club decided."