It depends on how accomplished and you need to speak with a divorce attorney (possibly) and a CPA/tax attorney (possibly) depending on which circumstances apply. For example, when you say "buy" you out my first question is wondering whether it is part of your property settlement as part of the current divorce...or has this stage already passed and the divorce is finalized and asset settlement phase behind you - meaning this is a NEW matter to address in which case it is no longer a tax-free property split as part of a divorce but a discrete gain/loss calculation of the home sale which will have a gain or loss depending on your cost in the home. If it is a gain it will be capital gain presuming you held the house over 1 year. In addition in all likelihood you will be able to avail yourself of the $250,000 gain exclusion for a primary residence which is an income tax rule requiring your CPA or tax lawyer's advice.
My answer is not intended to be giving legal advice and this topic can be a complex area where the advice of a licensed attorney in your State should be obtained.
Assuming you've lived in the home for 2 of the last 5 years and the gain on the proposed buyout would be less than $250,000 then there would be no tax on the capital gain. But there are several details that could impact this. IRS Pub 504 provides good guidance and covers most of them. If you still have questions, contact a tax professional to make sure. Better to have the issues resolved before the transaction takes place.
Evan A. Nielsen is licensed to practice law in California and handles federal tax matters throughout the U.S. The information provided here is for educational purposes only and is not intended as legal advice for a particular matter. This response does not create any attorney-client relationship with the author. For specific advice about your particular situation, please consult an attorney.