The Bosnians will feature in their first ever major tournament in 2014, having qualified for football's most prestigious competition as Group G winners in the European zone.
Begovic, who is rated as one of the best goalkeepers in the Premier League following his performances for Stoke City since 2010, believes that his side will leave their mark in South American next year,
"Our success is already guaranteed with a trip to Brazil," he told SportSport.
"But believe me, we're not going there for recreational purposes, we are going to play, to fight for our country and we will try to achieve the best possible result.
"I hope everybody will be fit for the World Cup. If so, then everything will be possible in Brazil."
Meanwhile, Sead Kolasinac has received clearance from FIFA to play for Bosnia at senior international level.
The 20-year-old, who was born in Karlsruhe, has played for Germany at the Under-18, Under-19 and Under-20 levels, but he will now represent the country of his parents.
"For us it is a great thing that we got such a player," Bosnoa coach Safet Susic told Agencija Fena. "I'm familiar with his abilities.
"He also plays regularly for Schalke, which tells a lot about him. He will probably made his debut in friendly against Argentina.