There is no need to remove the brain from the head and no need to transplant into a robotic body.
The critical thing is connecting the brain to external computer gear. What good would extended life be without sight/hearing/touch/taste/smell ? We don't have the tech just now to handle the interfacing but it's coming along quickly.
A brain could be kept alive for a time now without a body... but without I/O there is no point.
At some point it will be possible to grow a new body and place the brain within it. Nanotechnology will enable such things. Surgical skills are far too crude to connect a brain to a new body..it will take nano robotic skills to do such things. Human hands are much too crude and slow for such advanced work. Once nanotech enables working at the cellular level then almost anything is possible...nerve repair, organ and limb rebuilding..etc.
Once the modern digital computer was conceived we were set on a path to immortality. Thanks go to these two guys :-)
The computer is an amplifier for the human mind... it will allows us to do amazing things...the technology is still in its infancy.