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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Selby was ringside in Brooklyn to see Frampton beat champion Leo Santa Cruz on points to win the title.
Frampton wants to defend the title in his home city of Belfast and did not rule out a rematch, although he also has Selby in his sights.
"He's mentioned me a few times, sounds like he wants the fight," Selby said.
"I want the fight and it shouldn't be too difficult to make."
Selby said any possible meeting could be held in Belfast or Cardiff's Principality Stadium.
Barry-born Selby insisted before the fight there was no chance of him meeting British rival Josh Warrington, who beat Patrick Hyland to retain his WBC International featherweight title.
Selby accused Warrington of 'running scared,' after talks fell through over arranging a summer contest at Leeds' Elland Road.
Frampton inflicted the first defeat of 27-year-old Mexican Santa Cruz's career to become the first Northern Ireland fighter to win a world title in two weight divisions.
It was Frampton's first pro bout at featherweight, having moved up a division after unifying the IBF and WBA super-bantamweight titles by beating England's Scott Quigg in Manchester in February.
Selby said he was not surprised by Frampton's majority verdict over Santa Cruz, who has held world titles at three weights.
"I thought it was a brilliant fight and very competitive from the first bell to the last," Selby added.
"Carl Frampton boxed excellent and he surprised me with his tactics. I thought he would box on the back foot and use his range and jab.
"But at times he held his feet, stood in the middle of the ring and went toe to toe and beat Santa Cruz at his own game."
Nottingham Forest have signed striker Jason Cummings from Hibernian for an undisclosed fee on a three-year deal.
[NEXT_CONCEPT]
IBF world champion Lee Selby is confident his next fight will be against new WBA world featherweight champion Carl Frampton.