I think there's three ways to go about it:

Complete cell regeneration at full functionality. Think of our cells as batteries... When we're at the prime of our lives, they are regenerating back at 100%. As we get older, the battery wears down and that percentage starts to drop--giving us age related issues and appearance.

However if one were to fix this, I think cancer would be essentially cured, because that is when a cell of a certain area generates malignantly. That's also why cancer is more prominent in older people than young. Making it so cells continue to regenerate at perfection would eradicate cancer from the system completely.

The second, and what I think is the most unlikely, is the ship of Theseus method of replacing human parts for technological. We see people get new arms and legs all the time but those replacements have limited functionality and aren't really designed to be a true part of a person. People are looking more like techy pirates than the terminator or androids from DBZ. The biggest issue would be to create a working system that replicates the circulatory system and brain functionality. The human brain is so complex it will likely never be relocated, thus eliminating this as an option.

The third and most likely is the brain in a bar idea... A combination of psycho pass and inception. Essentially tricking the brain into believing time is moving at a much slower rate or creating a different reality perceived.

Let's say a brain can live up to 120 years max, that's really all anyone needs if they are hooked up to a machine that that tricks the brain into thinking every true hour the goes by is actually a lifetime in a false reality. If scientists can come up with a way to trick our brains into falsely perceiving time-- we could live a new life every "real day" our brains are hooked up. Now what if the technology gets better and we can live 1000 lives in a real day? Or an hour, or a minute. You get the idea. That could virtually be immorality.