Ben Stokes will remain as test captain with Harry Brook his vice-captain and Rob Key will stay as managing director of England's men's cricket following an ECB review centred around a humbling Ashes series.
England suffered a 4-1 defeat in Australia this year and the criticism included their casual preparations for the marquee series.
They lost to eventual champions India in the semi-finals of the Twenty20 World Cup this month led by Brook, whose altercation with a nightclub bouncer in New Zealand last year continued to be a distraction.
All-rounder Liam Livingstone has also criticised the team culture, saying the current regime does not care about players outside the core group.
"I've seen the driving ambition and determination that we're lucky enough to have within our leadership group to take the lessons from the Ashes and move forward," ECB chief executive Richard Gould told the BBC.
"These are all individuals that have got other things that they can do in their lives. They are all committed to doing the best for England and to learning the lessons that are evident."
British media have also reported that former New Zealand captain McCullum's bond with test captain Stokes had frayed during the Ashes series, though the duo have publicly backed each other.
McCullum is contracted to oversee the team until the end of the 50-over World Cup in South Africa, Zimbabwe and Namibia next year.
England host New Zealand for a three-test series in June before eight limited-overs matches at home to India.
Key, whose position had also come under scrutiny, told Sky Sports on Monday that McCullum was the best man to lead England.
"Ultimately, it's about who do the players, who do we think can take English cricket forward? Who's the one that can get the best out of the best players in this country? And for me, that's Brendon McCullum," Key said.
"There's been some really, really good stuff done. You know, it was a winter that did not go well, which would be an understatement, but that doesn't mean they're bad leaders."
Asked if McCullum needed to abort the ultra-aggressive, front-foot style known as Bazball after it was found wanting in the Ashes and at home to India last year, Key said it was more a matter of evolution.
"There's no point in keeping Brendon McCullum if you want him to completely change and become someone else," Key said.
"If you lose authenticity as a coach, captain, leader in any business, you're done. Brendon has not done that, and I don't want him to do that."
