The 21-year-old scored 23 goals in 39 appearances last season to help Hibs to the Scottish Championship title.
Former Scotland Under-21 international Cummings moved to Easter Road in 2013 and in total struck 69 times in 148 matches in all competitions.
He also helped Hibs lift the Scottish Cup in 2016 and moves to a side managed by former Rangers boss Mark Warburton.
"It is a massive club and I played against the manager's team a couple of years ago and I like the way they played," Cummings told the Forest website.
"I had a couple of mates in his team then and they only said good things about him so I am looking forward to playing under him.
"I want to play football and score goals and the way that the manager's teams play, they normally create a lot of chances so I feel that I am in the right team to create chances and hopefully I can get a few goals."
Cummings signed a four-year contract at Hibs last July following the Edinburgh club's first Scottish Cup win in 114 years.
"Jason goes with our very best wishes," said chief executive Leeann Dempster.
"He made a major contribution to our season in gaining us promotion back to the Premiership."
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Nottingham Forest have signed striker Jason Cummings from Hibernian for an undisclosed fee on a three-year deal.