Andrew, who has been a free agent since leaving Crystal Palace in the summer, has put pen to paper on a deal at Vale Park that runs until January 26, 2013.
The 25-year-old came through the youth ranks at Luton before joining Palace in the summer of 2008.
He had loan spells at Brighton, Millwall, Swindon and most recently last season Leyton Orient during his time at Selhurst Park.
"Calvin is a tall, strong forward who has experience of playing in divisions higher than League Two," said Vale boss Micky Adams. "I believe he will be an asset to our squad and I am looking forward to working with him."