According to LegalZoom, a person who wants to legally take on another person's car payments would have to take out a new auto loan, and the person would then need to have the title transferred from the owner to him or her. In addition, the owner has to pay off the entire car loan before the transfer can take place.
CarsDirect suggests that a loan swap in done in which a person gets a loan for the vehicle's full purchase price, and then pays the original owner for the car using that money. The original owner can use the money received to pay off his or her car loan, and then the title transfer can be done to give the car's title to the new buyer.
It's important to note that the person who gets the new loan has to be able to meet all the bank's requirements, including having a suitable credit score and an income that is sufficient for paying the monthly loan principal and interest. Otherwise, the loan swap won't be able to take place. Another thing that needs to be taken care of is the insurance policy for the car. The new owner will have to take over that policy, so the car insurance company must be contacted for the exact procedures on how this is done.