Anderson returned to the Test team earlier in the summer after McCullum was appointed as head coach and Stokes was named captain.
The new attacking England side swept New Zealand in a three-match series before seeing off India in the delayed fifth Test early in July.
They return to action on Wednesday at Lord's for the start of a three-match series against South Africa, and Anderson was eager to get back into the Test environment.
"I've been itching to get back in the dressing room to be honest," said the 40-year-old, who has played 172 Tests since making his debut in 2003.
"Those four Tests were incredible. Obviously what we did on the field was great, but the energy in the dressing room was brilliant.
"I felt as happy as I have done in an England dressing room for a number of years, so the last five weeks I've just been itching to get back in there."
While England's attacking approach has been lauded by players and drew widespread praise for some thrilling Test-match conclusions, its longevity has been called into question.
"I don't think it has to come unstuck at all," he said.
"If we keep working hard at what we're doing we now know we've got the ability to chase anything down and we've got the ability to take wickets in any conditions.
"If we keep playing with that entertaining sort of mindset and also be smart with it as well…there may be times when we can't go hell for leather with the bat and maybe we have to soak up a bit of pressure at times and just be smart about when we put pressure back on the opposition.
"I think that's the biggest learner from the last four Tests we've played, that we can be smarter at times.
"I think if we add that into our already entertaining mindset and be proactive and aggressive in the nature we play I think we can keep doing it."