Rautenbach will leave the Exiles this summer after seven years at the Premiership club.
And the Exiles on Thursday confirmed that 28-year-old Griffiths will be part of their squad for next season.
Griffiths made more than 100 appearances for the Swansea-based Ospreys, helping them to three league title successes.
"Cai is very solid at the set-piece, which is crucial when signing a tighthead prop," London Irish rugby director Brian Smith said.
"He is a direct replacement for Faan Rautenbach, who is leaving London Irish after seven years' service."
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.