In joining the Scuderia, it means Vasseur is almost certain to be in direct conflict with his Mercedes counterpart both on and off track.
Wolff was often at odds with Vasseur's predecessor in Mattia Binotto when it came to arguing for their team's best interests.
Asked of Vasseur whether he was prepared to ‘throw Wolff under the bus' to get Ferrari ahead in any title battle, he replied: “I know that we will fight on track, fight in the stewards, fight in the FIA, fight for the Concorde Agreement, and this is life.
“But at the end of the day, for the global picture, it's an advantage to have good collaboration between teams.
“On this side, when the common interests of the teams, of F1, is to have a discussion, to find an agreement, it will be a huge advantage to have a good relationship, but you know I also have a good relationship with a couple of other colleagues.
“This is always good, and then we have to be clever enough to speak completely our life, and then be sure I will fight like hell with Toto out on the track.”
Vasseur quickly under the spotlight at Ferrari
After just four weeks in his new role, Vasseur is effectively still finding his feet at Maranello in trying to understand what many perceive to be a complex organisation.
From the outset, the pressure will also be on Vasseur to deliver and end the Scuderia's long wait for a title, with the last drivers' championship in 2007 and the constructors' crown in 2008.
As to how quickly he can stamp his vision on the team and get it to run as he wants, he said: “First, my approach to racing is that we have to do a better job more than today.
“If today you say the team is in good shape then you are dead. You always need to have the mindset to say ‘Okay, where can we improve?' We always have to do something.
“What I bring to the team is the experience I have after 32 years on the pit wall, with racing spirit.
“It (Ferrari) is a proper team of racers but I will bring my own experience, and then it will be a no-name process.”