Stuart broke into the League with the Sharks in 1999 after being a first-round pick, No. 3 overall, in 1998.
With the deal, the Sharks now maintain -- until July 1 --the exclusive negotiating rights to Stuart, who has spent the past four-plus seasons with the Detroit Red Wings.
San Jose sent depth forward Andrew Murray and a conditional draft pick to Detroit for the rights to Stuart.
"We are very happy to acquire Brad's rights prior to July 1 and are hopeful that we come to an agreement on a new contract," said Wilson. "Brad is a player we are very familiar with -- a physical, team-first defenseman who is tough to play against, which is exactly the kind of mentality we want our team to possess."
Stuart, 32, had 21 points and a plus-16 rating for Detroit this past season. He also led the team in hits and was second on the team in blocked shots. For his career, Stuart has played in 876 games across 13 years with San Jose, Boston, Calgary, Los Angeles and Detroit. He has 305 points (74 goals, 231 assists) and 489 penalty minutes.
In the Stanley Cup Playoffs, he has 37 points (nine goals, 28 assists) in 124 career playoff games and has made the Stanley Cup Final two times, winning it all in 2008.
Murray, signed by San Jose as a free agent on July 19, 2011, played in 39 games with the Sharks last season, posting four points (one goal, three assists).
There has been intense speculation that Stuart would look to move West once he reached free agency, so the Red Wings managed to obtain something tangible for an expiring asset.
Still, this is another blow to the defense of the Red Wings, who are still reeling from the retirement of Nicklas Lidstrom just this past week. The Wings have now lost half of their top-four defenders from last season and will be on the lookout for reinforcements this summer.