TL;DR

I could not find an existing action to do this, so choose to use script.

*Download it if you are too busy. *

Create an Automator Application like this:

The script is:

fileList=""
for file in "$@"
do

filename="$file"
sips -s format jpeg -s formatOptions normal "$file" --out "${filename%.*}.jpg"

rm $file

done

Save the Application anywhere. Drag images on it, it will start to process.

*Note: This script will convert and compress image in place. *