The England Under-16 and Under-18 conference squad member has agreed a 12-month deal with the Championship outfit, where his older brother Jack is already an established member of the squad.
The 19-year-old made his first-team debut for the Tigers in 2009 and Nottingham director of rugby Glenn Delaney is pleased to have lured him to Meadow Lane.
"He is a very exciting player and will bring added depth and ability to our back line being able to play in many positions in the backline," Delaney told the club's official site.
"I believe Joe will fit very well into our club and having Jack here will help with his transition to Nottingham."
Cobden follows Joe Duffey in making the move to Nottingham in the summer, with the hooker having played for Leicester last season.
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.