Tuilagi, the 25-year-old brother of England centre Manu, has long been linked to a switch to Rodney Parade.
However the Dragons have now been given the green light to sign the former Leicester, Leeds and St Helens centre.
Director of rugby Rob Beale said: "This has been a very long process for the Dragons and for Andy.
"I know there has been media speculation over the past couple of months, but we had to ensure that this deal was done properly and that Andy had the necessary documentation in place before the signing was made.
"Having said that, Andy's reputation speaks for itself and I am confident that the wait will be well worth it."
Having finally got his man, Dragons head coach Darren Edwards is looking forward to seeing the Samoa international in action.
"Andy is exactly what we want in our back line," said Darren Edwards.
"We were keen to look at the strengths we have within our squad and make careful signings based on players who we feel will add to our game. Having worked with Andy at Leeds, I'm very aware of his qualities as a player and am confident that he will be successful at Rodney Parade.
"We have a great deal of skill and pace in our backs and Andy will bring a physicality and a line-breaking ability that will really complement our current squad."
Tuilagi made 42 appearances over three seasons for Sale, despite a layoff with a broken arm.
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.