McGregor used a hand to prevent Simon Mensing's shot crossing the line and was shown a red card before Stevenson sent Hutton the wrong way from the spot.
Mensing twice went close to extending the lead before midfielder Alex Neil went off injured for Hamilton to be replaced by Mark Gilhaney.
Clyde were fortunate to survive another penalty claim when Chris Higgins appeared to handle in the area, but referee William Collum was uninterested.
But the second goal was not long in coming as left-back Brian Easton went on a 60-yard run before pulling across for Offiong, who showed good footwork before dispatching the ball beyond Hutton.
Mensing set up Offiong early in the second half, but the latter shot high over the bar as Clyde struggled to contain their hosts.
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Christian Smith then cleared off the line from another Offiong shot following some poor Clyde defending.
Hamilton's James McCarthy showed some excellent skill to set up Gilhaney, but Hutton saved well from the substitute.
Gilhaney came close again before the 4,940-strong crowd began the celebrations at the final whistle.
Hamilton, who had been tracked by Dundee at the top of the table, return to Scotland's top flight for the first time in 19 years, while Clyde slip into second-bottom place in the table.
Hamilton Accies boss Billy Reid:
"This is the first time that Hamilton Accies have won any championship on their own territory. It means so much to me.
"I thought my players today were magnificent. Over the season I think we deserved to win the championship.
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"I've been runner up so many times and I feel for (Dundee manager) Alex Rae and (assistant) David Farrell for what they've put into it this season. I know how it feels. They've done a fantastic job there and they deserve credit as well.
"We will continue to blood young players, whether we're in the Premier League or not. This won't be the end of us playing young players just because we step up to the SPL.
"I think (James) McCarthy and (James) McCarthur are going to be fantastic players in the future. They're not going anywhere, they've got a year on their contracts to go.
"This club's not going to hold anyone back. It's about progressing young Scottish players and we'll enjoy the moment."
Hamilton:
Cerny, Stevenson (Swailes 89), Easton, Mensing, Elebert, McLaughlin, McCarthy, McArthur, Offiong (Waterworth 68), Neil (Gilhaney 31), Graham.
Subs Not Used: Taylor, Halliwell.
Goals:
Stevenson 21 pen, Offiong 43.
Clyde:
Hutton, Neil McGregor, James Gibson, Higgins, Bestvina, Wilson (Billy Gibson 54), Bradley (McKay 76), Ruari MacLennan, McSwegan (Arbuckle 46), Clarke, Smith.
Subs Not Used: Masterton, Cherrie.
Sent Off:
Neil McGregor (21).
Booked:
McSwegan.
Att:
4,940
Ref:
William Collum.
