When handled properly it is not a taxable event. Talk to the firm where the account is kept on how to do it. You'll first have to re-register the account in his name. Then he will transfer shares of the stocks and mutual funds to a new account in your name. Your son's cost basis in the shares transferred become your cost basis.
You'll probably have some paper work, as it is not usually done this way. The funds are legally his. Your son may be required to file a gift tax return, as he will be making a gift of his shares to you.
"Gift Tax" is somewhat of a misnomer. Even though a
gift tax return may be required, very few people ever actually pay federal gift
tax. The purpose of the gift tax return is usually only to document a reduction
in the allowable estate tax exemption.
See https://turbotax.intuit.com/tax-tools/tax-tips/Tax-Planning-and-Checklists/The-Gift-Tax-Made-Simple/...
