The former Colchester winger, 29 on Saturday, has joined the club until the first game of 2007 against Hull City.
Andrews is the second signing Wednesday have made after swooping for promising goalkeeper Shwan Jalal from Woking on a month's loan yesterday.
Laws is happy to sign the duo and Andrews especially will provide cover for suspended duo Chris Brunt and Wade Small while Jalal's move could come permanent if he impresses.