How do I remove a negative report from a collection agency.

American Express turned my account over to a collection agency. I was making payments, but then they took me off the hardship program and I could not afford to pay the minimum amount.
They sent the debt to a collection agency. I negotiated a pay off with the collection agency and have received a letter from them stating the account is closed. I also received a short note from American Express stating the same.
How do I get the negative report off my credit reports?
This was all debt relating to my business that has since closed and a partner who left the business leaving me with all the debt.