Rodman scored four goals in 25 matches for the Welsh side last term but rejected a new contract.
The 29-year-old played under recently-appointed Notts boss John Sheridan at Newport during 2015-16 and told the club website: "I know how he works.
"I know how he likes to play and what he wants from his players, and that was a big factor in me coming here."
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League Two side Notts County have signed Alex Rodman following the winger's departure from Newport County.