Brown set to join New Zealand squad
The 29-year-old All Whites vice-captain and midfielder suffered the injury in a warm-up game against Australia on May 24 and underwent surgery to repair the break.
He has now been passed fit to travel to the tournament that starts on Friday and will continue his rehabilitation programme in South Africa.
"Tim is a vital member of the squad on and off the field and he has been instrumental in creating our strong team culture," coach Ricki Herbert said in a statement. "He's made a remarkable recovery."
Brown's recovery is a boost for 78th ranked New Zealand but it was uncertain if he will be ready for the team's opening game in Group F against Slovakia on June 15.
New Zealand, in their second World Cup, also face defending champions Italy on June 20 and Paraguay on June 24.