My brother is 85 years old and wants to transfer his home to his son who has lived with him for many years.
How can this be done without either one of them having to pay inheritance taxes?

You could title it as joint or create a trust and place it in that or more. How is the house currently titled if you know and is any money owed on it right now?

You might want to consult an attorney who specializes in Senior affairs. I know where I live we have several attoneys who do just that,they set up trusts, living rights in the home, etc

First, there are no inheritance taxes to worry about on this. But there is the possibility of having to pay a gift tax. If your brother gifts the house to his son he will have to file a gift tax return in April, but he will not actually owe any gift tax unless the value of the house exceeds $1 million, or unless he has previously filed gift tax returns and the sum of all previous filings plus this one exceeds the $1M lifetime exclusion. However, I agree with the previous posters that it is a good idea to consult an estate planning expert who can determine the best course of action to fulfill your brother's wishes, especially if the value of his estate (inlcuding this property) exceeds $1M.