Recursive asynchronous file read - returning a promise on finish

I want to call a function that will iterate over files in a directory recursively, and return a resolve/reject on end. How can I do this?

readRecursive(location, (filename, content) => {
   writeChanged(filename, content);
})
.then(() => {
   console.log('Done!');
});

This is what I want to do - for each file, change something and rewrite it. And do something afterwards.

var readRecursive = (destination, callback) => {
    fs.readdir(destination, (err, filenames) => {
        if (err) {
            console.error(err);
            return false;
        }
        filenames.forEach(filename => {
            fs.readFile(destination + filename, 'utf-8', (err, content) => {
                if (err) {
                    console.error(err);
                    return false;
                }
                callback(destination + filename, content);
            });
        });
    });
};

The problem is that if I return the promise here, it will call then after the first file is read, and skip the rest. What's the best way to solve this?

via user99999