You normally don't owe tax for giving a gift. However, if the gift is more than $14,000 in a year, you must report it to the IRS on a gift tax return. You have a lifetime gift limit of $5.4 million; after that you would owe tax, and the gift tax return documents your gifts for the IRS to track against your limit.
Your niece will receive your cost basis in the home. Cost basis is used to calculate any capital gains tax that she owes when she sells it. If she can't prove a cost basis, the IRS will assess higher taxes against her, so it will be helping her greatly to give her proof of your cost basis. That is the original cost you paid for the home, plus the value of any permanent renovations and improvements, and minus depreciation you took or could have taken when it was a rental.
You would have no further tax liability as far as the IRS is concerned, but you would likely be personally liable on the mortgage even after you give away the home, until it is paid off or refinanced. (In other words, I'm sure your niece is a nice person, but she could trash the house and stick you with the bill.) And the mortgage will stay on your credit report until it is refinanced in her name or paid off. And giving away the house may be grounds for the mortgage company to demand immediate repayment.
