Johnson, 37, played alongside Haworth at Wigan Athletic and worked under him as assistant manager during a two-year spell in charge at Clitheroe.
He has been at Marine, one of his former clubs from his playing days, as part of the first team coaching staff under Neil Young since May 2018.
Haworth said: "I’m delighted that Jonno has joined us at Stalybridge.
"He worked with me at Clitheroe and went to Marine to gain some experience in a different environment.
"We are very happy for him to join us at Celtic."
Johnson added: "Simon and I go back nearly 20 years from our time at Wigan Athletic together and we've previously worked together at Clitheroe.
"When he asked me to join his staff again it was an offer I couldn't turn down.
"I’ve been at Marine the last two seasons with Neil Young who I have great respect for and friendship with, I just want to thank him for everything he's done for me.
"Regarding the new season I can't wait to get going again with Simon and the lads whenever that may be! Hopefully in the not too distant future."
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