The disabled actor, who plays Ryan Stocks in Yorkshire soap Emmerdale, said: "I never thought I would be here. This shows the progression that we need in this day and age. This means the world to me."
Ant and Dec won the Best TV Presenter award at the ceremony.
Ant McPartlin said: “This is a genuine shock, especially this year.
“We want to say thank you to everybody. I really don’t think that I can accept this award this year.
“The one reason we won the award this year is this guy: his hard work, his wit, his dedication. Best mate in the world. I love this guy.”
Declan Donnelly said: “I’ve got him back now, and now we’re back together.
“Special thank you to Dermot who said he was going to chuck in the towel if we won this year.”
This Morning scooped the Best Daytime show honour at the awards.
The programme fended off competition from fellow ITV show Good Morning Britain, hosted by Piers Morgan and Susanna Reid.
Morgan was filmed close up on the ITV coverage of the awards ceremony, and did not look pleased with the outcome of the viewers' vote.
Schofield said on collecting the award: "Thank you so, so much for voting for us. We never take it for granted. Our This Morning family are amazing. Our viewers are part of the This Morning family."
Willoughby added: "This is a special year for This Morning."
Both hosts expressed how "lucky" they were to work with each other every day, and thanked the staff of the show.
Richard Madden claimed the award for Best Drama Performance for Bodyguard, and thanked his female co-star saying: "The biggest thank you goes to Keeley Hawes. You couldn't ask for a better, more talented actress."
Bodyguard also won in its own right, being named the Best New Drama.