Dire Straits, Bon Jovi and The Cars will also be inducted along with jazz singer Nina Simone and the “godmother of rock ’n’ roll” Sister Rosetta Tharpe.
The six acts were chosen from 19 nominees that included Radiohead, who had been tipped to enter the hall of fame in their first year of eligibility.
Hayward said: “It’s a privilege to be celebrated in the same building as my own heroes – Buddy Holly and the Everly Brothers – and with my heroine Nina Simone.
“I’m extremely grateful to the Rock and Roll Hall of Fame, first for creating the supreme temple to all that has brought endless joy into my life since I was a small boy, and now, after all these years, for including us.
“But all the thanks must go to The Moody Blues’ fans for giving us a wonderful, wonderful life in music.
“Our induction has now validated the music they so love and I’m so, so pleased, for us all.
“Yippee.”
Formed in Birmingham in 1964, The Moody Blues pioneered art rock and are most famous for their 1967 hit Nights In White Satin.
They will be inducted in Cleveland, Ohio, next April alongside the five other acts.
Votes are cast by about 1,000 music industry figures and by fans online.