Many of the answers using eval and echo kind of work, but break on various things, such as multiple lines, attempting to escaping shell meta-characters, escapes inside the template not intended to be expanded by bash, etc.
I had the same issue, and wrote this shell function, which as far as I can tell, handles everything correctly. This will still strip only trailing newlines from the template, because of bash's command substitution rules, but I've never found that to be an issue as long as everything else remains intact.
apply_shell_expansion() {
declare file="$1"
declare data=$(< "$file")
declare delimiter="__apply_shell_expansion_delimiter__"
declare command="cat <<$delimiter"$'\n'"$data"$'\n'"$delimiter"
eval "$command"
}
For example, you can use it like this with a parameters.cfg which is really a shell script that just sets variables, and a template.txt which is a template that uses those variables:
. parameters.cfg
printf "%s\n" "$(apply_shell_expansion template.txt)" > result.txt
In practice, I use this as a sort of lightweight template system.