I worked on a massive line of business application replacement for a major national cable tv network. The new system development was done with SCRUM, it was about a 18-24 month development project to re-implement almost all the major sub-systems; which were approaching 10 years old.
There was a planning phase of like 6 months before the development started, but it was approached as SCRUM as well. This is where the product owner wrote high level stores and epics after existing system analysis and interviewing the customers.
The existing system was extremely stable as went into critical maintenance mode; only show stopper issues were fixed, everything just logged for historical purposes and to make sure the same issues didn't appear in the new system.
The new system evolved as described in an Agile process, it was extremely smooth for the most part. When the replacement system reached feature partity, it didn't go into production, but into parallel production trials. A sub-set of non-critical workers started using both systems, to validate that the new system behaved like the old one; with the old bugs fixed of course.
When the new system achieved almost 100% new features complete it was rolled out for general parallel production runs, which lasted a couple of months.
Once it was deemed by the customer to meet their needs, the old system was backed up, switched off and sat. I assume they have re-purposed the old system hardware because they never needed to revert to the old system after cut over.