Final answer:
The 'export' command is used to define and assign environment variables in bash, making them accessible to subprocesses initiated from the shell.
Step-by-step explanation:
The command that allows the definition and assignment of environment variables under bash is export. Using the export command, you can set an environment variable with the syntax export VARNAME="value". It not only defines the variable but also makes it available to subprocesses started from the bash shell. The env command, on the other hand, can be used to run a program in a modified environment, but does not by itself define a new environment variable.