The Java 8 API for Dates and Hours is tremendous. I use it and it is my favorite. You can use JODA as it says to you @Alejandro Rangel Celis, which is compatible with previous versions of Java.
Java 8
The way you have it is valid, but not entirely correct because you do not take into account the months. For this you can use the class Period :
import java.time.LocalDate;
import java.time.Period;
import java.time.format.DateTimeFormatter;
// 01/01/2000
DateTimeFormatter fmt = DateTimeFormatter.ofPattern("dd/MM/yyyy");
LocalDate fechaNac = LocalDate.parse("15/08/1993", fmt);
LocalDate ahora = LocalDate.now();
Period periodo = Period.between(fechaNac, ahora);
System.out.printf("Tu edad es: %s años, %s meses y %s días",
periodo.getYears(), periodo.getMonths(), periodo.getDays());
Exit:
Tu edad es: 22 años, 9 meses y 29 días