The 42-year-old will replace Matthew Mott, who stepped down following England's T20 World Cup semi-final exit against eventual champions India in June.
McCullum has extended his contract until the end of 2027, having begun his tenure in May 2022. His white-ball stint with England will start when they tour India in January.
Former England batter Marcus Trescothick will continue to serve as interim head coach for this month's series against Australia and the tour of the Caribbean starting in October.
"I've thoroughly enjoyed my time with the test team, and I'm excited to extend my role to include the white-ball sides," McCullum said in a statement.
"This new challenge is something I'm ready to embrace, and I'm eager to work closely with (white-ball captain) Jos (Buttler) and the team to build on the strong foundations that are already in place.
"Managing Director of England Men's Cricket) Rob Key's vision for the future of English cricket is something that really resonated with me," he added.
"The idea of a unified coaching structure, especially with the schedule easing next year, made perfect sense."
