Gosh, a lot of answers already. A simple and convenient route I found was to execute ROBOCOPY.EXE twice in sequential order from a single Windows command line instruction using the & parameter.
ROBOCOPY.EXE SOURCE-DIR TARGET-DIR *.* /MOV /MINAGE:30 & ROBOCOPY.EXE SOURCE-DIR TARGET-DIR *.* /MOV /MINAGE:30 /PURGE
In this example it works by picking all files (.) that are older than 30 days old and moving them to the target folder. The second command does the same again with the addition of the PURGE command which means remove files in the target folder that don’t exist in the source folder. So essentially, the first command MOVES files and the second DELETES because they no longer exist in the source folder when the second command is invoked.
Consult ROBOCOPY's documentation and use the /L switch when testing.