The former GMTV reporter and his dance partner Erin Boag left the competition after finishing in the bottom two alongside Westlife star Nicky Byrne and professional Karen Hauer.
In the dance-off, Arnold performed a salsa to a version of the Wham! hit 'Club Tropicana' and Byrne a jive to 'Jailhouse Rock'.
After both couples had performed their routines for a second time in front of the 6,000 spectators at London's Wembley Arena, Craig Revel Horwood gave his verdict.
"Just for sheer exuberance and energy, I am going to save Nicky and Karen," he said, opting to send Arnold home.
"Well, you both performed very well tonight, but for content and energy as well, I am going to save Nicky and Karen," added Darcey Bussell, making it two votes against the ITV presenter.
Bruno Tonioli added: "Both highly entertaining, but I have to go as well with power and content, and that was delivered by Nicky and Karen."
Following the announcement of the result, Arnold reflected on his experience and said: "I've loved it. Do you know, what is amazing about this experience is that this party is happening in millions of homes around the country.
"The one thing I'll take from it is that now when I walk down the street people no longer cross the road to avoid me! Now they smile, they want to chat."
"It's been amazing," he continued. "You guys here have been amazing... and to be part of this company of players has been amazing.
"I know where I'll be next week - it's my birthday - [and] I'll be with my godchildren, with my family and friends who have been going through the whole thing, and I'll be popping a cork and seeing who is here next week.
"It's extraordinary, this show just gets better and better," he added. "And one final thing - this is madam's [Erin] tenth series.
"A round of applause for Erin Boag, she has made the last two months fantastic. I always thought I'd miss the wardrobe most, but I don't think I will, I will miss Erin Boag."
Boag added: "Richard has made the last two months of my life a big joy. He's full of life and full of energy, and I'm really proud to have taught him... to have danced with [him] and to call [him] my friend."
Sunday's results show also featured a performance by Girls Aloud, who performed their track 'Something New'. Kylie Minogue also took to the stage and sang a special rendition of her '80s classic 'The Locomotion'.
Strictly Come Dancing continues on Saturday November 24 at 6.30pm on BBC One.
Photo gallery - Strictly Come Dancing week seven results show: