Steve Cooper's side was in the ascendancy in the first half and its reward at Wembley Stadium arrived when Colwill turned into his own net after 43 minutes.
Huddersfield was left aggrieved in the second half after referee Jonathan Moss did not award Harry Toffolo a penalty for a challenge by Jack Colback, and Lewis O'Brien had a strong case for a spot-kick too. The first was also controversially denied by the video assistant referee (VAR), which didn't deem the second incident worthy of review.
But Forest held firm to secure its return to the Premier League for the first time since the 1998-1999 season.
Forest made a promising start as Ryan Yates flicked a header narrowly wide from a James Garner free-kick.
Yates skewed another presentable chance over but the pressure from Cooper's side seemed to have subsided until just before the interval, when Colwill inadvertently diverted into his own goal following Garner's teasing cross.
Yates tamely fired into the hands of Huddersfield's Lee Nicholls after the break, while an unmarked Jonathan Hogg wastefully headed over from Sorba Thomas's corner at the other end.
Huddersfield grew into the game past the hour mark and Toffolo thought he had won a penalty but was instead booked for diving after going down under the challenge of Colback.
O'Brien had what looked to be a similarly strong appeal turned down after clumsy play from Max Lowe, leaving Huddersfield furious in defeat as Forest, which had to take off goalkeeper Brice Samba because of injury, gained promotion.
Twice European Cup winners in the days of Brian Clough, Forest will feel it has rightfully returned to the English top flight, while Cooper has finally won promotion through the Championship play-offs at the third time of asking.
He inherited a Forest side that was languishing in the relegation zone in the early stages of the season after Chris Hughton's dismissal in mid-September.
He has transformed Forest's fortunes, triumphing in 27 of his 45 games in charge at a win percentage of 60, the highest of any Forest manager to take charge of at least 15 games since the club joined the Football League in 1892-1893.
Forest can prepare for life in the big time, with the Premier League fixtures to be confirmed next month and the new season starting in early August. Huddersfield, meanwhile, will have to go again in the Championship next term.