Use the shell globbing syntax:
grep pattern -r --include=\*.cpp --include=\*.h rootdir
The syntax for --exclude is identical.
Note that the star is escaped with a backslash to prevent it from being expanded by the shell (quoting it, such as --include="*.cpp", would work just as well). Otherwise, if you had any files in the current working directory that matched the pattern, the command line would expand to something like grep pattern -r --include=foo.cpp --include=bar.cpp rootdir, which would only search files named foo.cpp and bar.cpp, which is quite likely not what you wanted.
Update 2021-03-04
I’ve edited the original answer to remove the use of brace expansion, which is a feature provided by several shells such as Bash and zsh to simplify patterns like this; but note that brace expansion is not POSIX shell-compliant.
The original example was:
grep pattern -r --include=\*.{cpp,h} rootdir
to search through all .cpp and .h files rooted in the directory rootdir.