The 28-year-old joined the Magpies last week in a deal thought to have cost the club £150,000.
Dennis scored 21 goals last season but could not prevent the Spireites from dropping out of the Football League and is eager to make up for it by winning promotion with Notts.
“I came back into the league with Chesterfield and had two relegations so that’s the last thing I want on my mind,” he told the Nottingham Post.
“I want to be at the opposite end of the table and right up there vying for promotion.
“I know Notts finished fifth last season and hopefully we can go one better, get automatic and get up into League One.”
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