The 20-year-old spent last season with the National League outfit.
He made 10 appearances for the Magpies last season before a ruptured Achilles ruled him out for the remainder of the National League campaign.
“I've been working hard over the past eight months to get fit and now I'm back," Graham told the club's website.
“I started training two weeks before lockdown and then had a hard programme to do at home every day.
“I've been training with the first team, which has been a great experience, and now it feels good to be back at Notts.
“As soon as I knew there was potential for me to come back I've been excited because I really enjoyed it.
“I know I've got strong competition for my place and that we'll always be pushing each other."
Welcome back, @samgraham1221!
— Notts County FC (@Official_NCFC) September 8, 2020
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