I am an F1 student, and I have been filing the form 1040 through an online software for the last three years. Someone had told me that I need to file 1040 since I meet the substantial presence test. Is it correct? I've been a F1 student for the last 4 years, and have been spending 9 months each year in the US. Am I supposed to be filing form 1040NR? If so, is there any way to correct the forms I filed for the last three years?

Yes, on F1 you are exempt from residency for 5-years. You must file non-resident tax return Form 1040NR or 1040NR-EZ and Form 8843. Your income is not subject to FICA taxes but you must pay federal and state income taxes.
Read: Your U.S. Tax Return: U.S. Tax Filing Requirements for Non-Residents (http://taxipay.blogspot.com/2008/03/us-tax-filing-requirements-for-non.html)

You need to file amended tax return Form 1040X along with properly done nonresident tax return and Form 8843.

Thanks for your answer. Will I be allowed to submit 1040X for all three years?

Yes, as per tax laws you must amend all you tax returns filed incorrectly.
Now the question is what happens if you do not amend? May be other tax experts have better knowledge.