The 63-year-old has penned a two-and-a-half year contract at Old Trafford, which will initially see the him act as interim manager.
The Red Devils, who earned a draw at Premier League leaders Chelsea on Sunday, have moved quickly to replace Ole Gunnar Solskjaer, who was sacked last Sunday.
And Neville believes Rangnick, who was most recently in charge of RB Leipzig, can revolutionise the club beyond the current campaign.
“Welcome to the Greatest Football Club in the World Ralf Rangnick,” Neville said on Twitter.
“A contract for six months to coach the team. A contract for two years to coach the club.”
Rangnick will now take charge at Old Trafford while the club hierarchy seeks a permanent successor to Solskjaer before continuing in a consultancy role.
“I am excited to be joining Manchester United and focused on making this a successful season for the club,” he said upon the announcement.
“The squad is full of talent and has a great balance of youth and experience. All my efforts for the next six months will be on helping these players fulfil their potential, both individually and, most importantly, as a team.
“Beyond that, I look forward to supporting the club’s longer-term goals on a consultancy basis.”
Football director John Murtough added: “Ralf is one of the most respected coaches and innovators in European football. He was our number one candidate for interim manager, reflecting the invaluable leadership and technical skills he will bring from almost four decades of experience in management and coaching.
“Everyone at the club is looking forward to working with him during the season ahead, and then for a further two years in his advisory role.”