Bowery, 25, scored twice in 18 appearances for Crewe during a loan spell from Leyton Orient in 2016-17.
"I think he improves us," said Alex manager David Artell.
Guthrie, 24, is set to join an unnamed League One club, while fellow out-of-contract defender Ollie Turton held talks over his future on Tuesday.
"I had a conversation with Jon and he told me that he wanted to leave, which was fine," added Artell.
"He said that we could have not have done anything more to convince him to stay."
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Crewe Alexandra have signed striker Jordan Bowery on a two-year contract, while defender Jon Guthrie is leaving after five years at the club.