How do you close joint credit cards ?

My x husband is now in a position to pay off the balances of credit cards that were assigned to him through our divorce agreement. He has mostly been timely on paying off this debt that he accrued and is going to pay off the balances in full. Since many of these cards have been open for over 15 yrs. and have both of our names on the accounts, what is the best way to close these cards so our credit scores don't take too much of a hit?