Yes, the team he is traded to owns the contract. AND IS BOUND BY THE TERMS OF THE TRADE ONCE APPROVED BY THE LEAGUE OFFICE. 
According to the league, each trade is taken on a case by case basis. So if the Packers added language to the trade agreement stipulating extra compensation in the event of another trade of Favre to the Vikings and the league signed off on it, the team in question would have to comply.
From the link:
A popular subject contained in various e-mails we've received over  the course of the day is a trade of Favre to a team other than the  Vikings or the Bears, followed by a trade of Favre to a team like the  Vikings or the Bears.
Don't count on it happening.  Our guess is that the Packers would  include in any trade of Favre to someone other than the Vikings or the  Bears a provision that, if Favre thereafter is traded to the Vikings or  the Bears, the compensation will increase to a first-round pick, or  more.
Though the Packers can't release Favre with an understanding that he  won't sign with certain teams, the Packers presumably can condition  compensation on what the team that acquires Favre's rights does with  them.
It's no different than, for example, the trade that gave the Broncos  a seventh-round pick that would have upgraded if Jake Plummer had  reported to the Bucs.  Or the deal that will send a fourth-round pick  from Tennessee to Dallas if Pacman Jones isn't reinstated for the 2008  season.
It's a conditional draft pick — and the condition that would  increase the compensation in the case of a Favre trade would be the  re-trading of Favre to a team like the Bears or the Vikings.
We asked NFL  spokesman Greg Aiello whether such a term would be enforceable, but  Aiello declined to speculate.  He said that the trades are considered  on a case-by-case basis, and that the league office would evaluate the  terms that are presented, if/when trade terms are reached. 
Peace.