In addition, Pele is the only player that has been on three World Cup winning teams.

(Why is 'has been' used? Can't we use ' was' instead of 'has been'?)

First of all, you should use "who" instead of "that" since Pele is a person, not a thing!

Present perfect tense indicates an action in the past that took place over time (not just a once-and-done action), maybe even up to the present time.

You can use "was" if you are sure he is all finished playing the sport.