Replace string in multiple files using find and sed

I assume that the string can contain any character except newlines and null bytes. You can quote the string for use as a sed pattern. The characters $*./[\^ need to be preceded by a backslash. In the replacement text, you need to quote the characters \&/.

regexp=$(printf %s "$old" | sed 's:[$*./\[^]:\\&:g')
replacement=$(printf %s "$new" | sed 's:[\&/]:\\&:g')
sed -e "s/$regexp/$replacement/g"

If you have Perl available, it's simpler.

export old new
perl -pe 's/\Q$ENV{old}/$ENV{new}/'

To act on all the files in the current directory and its subdirectories recursively:

regexp=$(printf %s "$old" | sed 's:[$*./\[^]:\\&:g')
replacement=$(printf %s "$new" | sed 's:[\&/]:\\&:g')
export regexp replacement
find . -type f -exec sh -c 'for x; do sed -e "s/$regexp/$replacement/g" <"$x" >"$x.new" && mv "$x.new" "$x"; done' _ {} +

or

export old new
find . -type f -exec perl -i -pe 's/\Q$ENV{old}/$ENV{new}/' {} +

Substitute "Some...\n...Thing" by the contents of file "new" in one or more input files

perl -i -p0e 's/Some.*?thing\n/`cat new`/se' input.txt ...

1. -i to change input.txt directly
2. -p0 slurp input file file and print it in the end
3. s/regexp/.../s in regexp . is .|\n
4. s/.../exp/e replace by eval(exp)
5. new -- a file containing the replacement text (This is completely...different text)
6. if useful you can expand the original text s/Some text\n...\n...thing\n/...