The 6ft 6in defender has been a commanding presence at the heart of the Borussia Mönchengladbach defence for the past two seasons, and hopes to transfer those qualities from the Bundesliga to the Premier League.
But first, Vestergaard says he must prove to his new coaches and colleagues that he is ready to take on such responsibility.
“I do like to be a leader on the pitch, but I have to find my role here first and earn the other players' trust," he said.
“I'm not expecting to come in here and tell the guys who have been here a long time what to do, but I will try to find a role in the team and eventually take more responsibility if it is also wanted by my teammates and by the coaches.
“I think it is important that my teammates accept me and respect me first, and that is my job for the next weeks and months – to earn their respect."