I don't believe the above answer is correct and is actually VERY misleading, especially for one of the top google results.
Pub 529 states that you must be a US Citizen OR a resident alien all year, and not file form 2555 (foreign income exclusion). So if you are a US Citizen living overseas, and properly report all your foreign income, without exluding it, then I believe you would qualify:
Rule 4—You Must Be a U.S.
Citizen or Resident Alien All
Year
https://www.irs.gov/pub/irs-pdf/p596.pdf
Also, the 6 month test that is mentioned above is related to the Qualifying Child test, not the overall EIC requirements. Therefore, your children may not come into the equation, which will significantly lower your income threshold to qualify and the amount of credit. Possibly reducing qualification at all.
If your kids are disqualified, the rules for the EITC for just you and your spouse are here:
https://www.irs.gov/credits-deductions/individuals/earned-income-tax-credit/claiming-eitc-without-a-...
If I'm wrong however, I would love to have the clarification, as this has been a sticking point for me for awhile.
