I live outside the U.S., and although I work for a U.S. company, I have claimed the foreign income exemption numerous times over the last 10 years. I have also been contributing regularly to a Roth IRA for myself and a spousal Roth IRA for my wife (who is not employed). I just learned that I was not eligible to make those contributions. I was wondering if someone could give me guidance in regard to how I can fix this problem with that I apparently now have with the IRS.

“I just learned that I was not eligible to make those contributions.”---->I assume that you are a NON-US person, then, No.In order to contribute to an IRA of any type, you must have earned income that yu earned in US that is otherwise taxable in the US.