Smith, 26, is a former Wales Under-21 captain who has made 60 appearances for the Ospreys.
London Irish head coach Toby Booth said: "Tom's ability to play at both blindside flanker and number eight means he will add further to our back-row options. He is a top class defender that possesses very good set-piece attributes."
Smith follows Leicester lock George Skivington in signing for London Irish and he will link up with the squad in the summer.
"I have thoroughly enjoyed my time at Ospreys but feel it is time to move on and I am keen to do this at London Irish," Smith said.
"There are a few Welsh lads in the current London Irish squad who have gone on to be extremely successful in recent seasons and I hope to follow suit when I join this summer."
The Exiles are losing lock Nick Kennedy to Toulon and scrum-half Paul Hodgson to Worcester.
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.
$29.99
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.
