McCullum replaced Chris Silverwood who left the role in February after England were thrashed 4-0 in the Ashes in Australia.
The 40-year-old, who scored 6,453 Test runs for New Zealand in his playing career, only has coaching experience in the Indian Premier League but was confident he could kickstart a turnaround for a side who have managed one win in their last 17 Tests.
"My job will be to try to take away some of the pressures initially, bring in some enthusiasm. Naturally, when there's some change, guys kind of get a bit of a lift anyway, so hopefully that will translate to performances early as well," McCullum told a media roundtable at Lord's.
"But first I've got to have a look around and see where things sort of sit currently and try and identify some areas where we might need to make some changes at times too, but I'm very much looking forward to the challenge."
There has already been a change in hierarchy on the field as Ben Stokes takes over as captain, succeeding Joe Root, who led the side in a record 64 Tests over five years but stepped down after the March 1-0 series defeat in West Indies.
McCullum captained New Zealand in 31 Tests and was part of the resurgence that led to them becoming a real force in the long game, eventually culminating in their winning the World Test Championship last year under his successor Kane Williamson.
With Stokes being such a talisman for England, McCullum said their relationship would be key in dragging the team up the Test rankings from sixth.
"I think the captain-coach relationship in cricket is vital. I think there needs to be a really tight bond there," he said.
"You don't have to be the best of mates, but I think you have to have a real clear sort of vision of where you want the team to go and you both align with that, and then when you have that, then you can try and just fill the gaps.
"It's my job as a coach to fill the gaps for Stokes. I want him to be the most authentic person that he can be, lead the way that he wants to be. There'll be times where I might have to pull him back and times where I might have to push him forward."
One problem has been how to blend youth with experience, with veteran fast bowlers James Anderson and Stuart Broad recalled to the side following their absence from the West Indies series.
McCullum said he would sit down and chat to both about their future plans but that they would still be valuable assets on and off the field.
"We should enjoy the fact we've got 280 Test matches sitting in our bowling unit and guys who have been there and done it before. It would be great if they were at the forefront of the next kind of development on the side," he said.
Asked if he could lead England to being the number one Test side in the world, McCullum pleaded for patience. "Yeah, definitely. That's what we're all aspiring to do. I think it's going to take a bit of time and we should hopefully get a natural uplift and results straight away and New Zealand's a good cricket team, but if we play properly, we'll give ourselves a good chance," he said.
After New Zealand, England will host South Africa in another three match series in August-September and also play a one-off Test against India in July.