Many children cross from right to left and vice versa when they first begin to write. The key is to allow him to pick which hand is most comfortable and encourage him to write with only one hand once he has made the choice. And there are some children who are equally as skilled with both hands, thus no choice needing to be made. In due time you will see his preference shine through.
This could be a blessing, he is ambidextrous. My son (5) switches from left hand to right hand, but seems to favor his left hand the most. Let him decide which is the most natural for him. If he is comfortable writing with his right hand and it's age appropriate legible, I wouldn't concern myself. However, if he prefers to write left handed, then allow him to practice and make that decision for himself. He may write with his right hand but choose to bat with his left, etc. It's not that big of a deal and he's old enough to decide which is best for him. Best wishes!