He cannot do that without marrying you first, or terminating your rights as a mother.
I am exclusively a family law attorney, practicing primarily in the metro Atlanta, Georgia trial courts. However, I handle appeals from anywhere in Georgia.
Unless you are willing to surrender your own rights and make him the only legal parent, which I am assuming you don't want to do, you will have to be married and do a stepparent adoption. If you were to get married, and the biological father has no interest in being a father, you could do a stepparent adoption fairly easily with the help of an experienced adoption attorney. If marriage is not in the cards, best to leave things as they are.
The above information is general in nature. In order to obtain more specific and legal advice upon which to base your important decisions, please contact our office directly for a free phone or in person consultation. Robert M. Gardner, Jr. Hicks, Massey & Gardner, LLP email@example.com 53 W. Candler St. Or 718 Oak St. Winder, Ga. 30680 Gainesville, Georgia (770) 307-4899 (770) 538-0555 gadebtlaw.com hicksmasseyandgardner.com serving metro Atlanta and all of Northeast Georgia Bankruptcy, Divorce, Personal Injury, Worker’s Compensation, Medical Malpractice, Adoption, Civil and Criminal Litigation
The advice of the first two answers was basically good, but not totally accurate. While stepparent adoption normally does require that the petitioner (stepfather) be married to the biological mother, the judge have the power to that requirement. If there is some good reason for that (beyond what is stated in your question I mean), the judge be willing to do that. But having said that, it's not likely. As stated, consulting an experienced adoption attorney is highly advisable.
If your boyfriend were to adopt your child, your rights would be terminated and you would cease to be the mother.
If you want to remain the mother, the only way for you to have him adopt would be for him to marry you first. Once he does that, then you need a lawyer.
If you find this answer helpful, please mark it here on AVVO as helpful. In answering you, I am attempting to communicate general legal information and am not representing you. Do feel free to call me at 404-768-3509 if you wish to discuss actual representation (the phone call also does not retain counsel; that requires an office visit and appropriate paperwork). In that a forum such as this provides me with limited details and doesn't allow me to review details and documents, it is possible that answers here, while meant to be helpful, may in some cases not be complete or accurate, and I highly recommend that you retain legal counsel rather than rely on the answers here. (You can also email my office at firstname.lastname@example.org . An email also does not retain my office, but can help you get an appointment set if you prefer not to call). Any information in this communication is for discussion purposes only, and is not offered as legal advice. There is no right to rely on the information contained in this communication and no attorney-client relationship is formed. Nothing in my answer should be considered as tax-advice. To ensure compliance with IRS Circular 230, any U.S. federal tax advice provided in this communication is not intended or written to be used, and it cannot be used by the recipient or any other taxpayer (i) for the purpose of avoiding tax penalties that may be imposed on the recipient or any other taxpayer, or (ii) in promoting, marketing or recommending to another party a partnership or other entity, investment plan, arrangement or other transaction addressed herein. I am also required to advise you, if your question concerns bankruptcy, that the U.S. Congress has designated Ashman Law Office as a debt relief agency that can help people file bankruptcy.