The Belfast-born tighthead, who has also represented his country at Under-21 level, originally joined Exeter from Ulster in 2007 and made 44 appearances before moving to Harlequins in 2009.
Andress, 28, returned to Devon this season and has featured 12 appearances in his second spell with the Chiefs.
Forwards coach Phil Davies said: "I have known of John for a long time and actually looked at signing him when I was with the Scarlets so we are delighted he will be joining the Warriors next season.
"He has a lot of experience behind him and this is an opportunity for him to come into the club and really put that experience into action.
"John is an outstanding scrummager and good ball handler around the field, a true all-round and knowledgeable forward."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.