A 1-1 home draw with Brighton and Hove Albion was enough to send Boro up behind champions Burnley, with Chris Hughton's side missing out on goal difference.
Karanka claims his detractors considered him "crazy" for targeting promotion when he took charge in November 2013, and could not hide his delight at ending Boro's seven-year exile from England's top flight.
"I've been coach for two-and-a-half years. I can't be more proud of this group of players, this crowd and this chairman. It's amazing," he told Sky Sports.
"When I arrived here, some people said I was crazy when I said my aim was to take this club back to the Premier League. Two-and-a-half years later, we are in the Premier League."
Striker David Nugent, who set up Cristhian Stuani's goal in Saturday's draw, paid tribute to chairman Steve Gibson for his work in transforming the club's fortunes.
"It's a great feeling," he said. "We've been working all season for this. It's means so much to this club.
"The chairman deserves it because he's worked so hard to get this club back into the Premier League. This one's for the chairman."
Winger Stewart Downing, who rejoined his boyhood club last July, added: "Middlesbrough never make it easy, but it's incredible.
"The chairman was one of the big reasons why I came back here and he deserves it more than anyone."