Henson, 30, has been without a club since April after being sacked by Cardiff Blues over his drunken behaviour on a flight returning from a game in Glasgow.
But Henson worked with Exiles coach Lyn Jones during his time at the Ospreys and has been given the latest in a series of chances to get his career back on track.
Jones said: "Gavin has a great talent but over the past three or four seasons he has not realised his full potential for a number of reasons that are well documented.
"I sincerely hope and believe he can now draw a line under that period and move forward again with London Welsh."
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.