The new couple have apparently nicknamed themselves Chlam - combining their two names - after Madeley finished her relationship with Glenn Crickmar.
A source told the Sunday Mirror: "They clicked straight away and became good friends - but one thing has led to another and they are now regarded as an item by the cast and crew on Dancing on Ice."
The pair allegedly became even closer after visiting Sheffield this week to rehearse for the show's tour. They were spotted flirting with each other during a cast trip to Avenue Q at the Lyceum Theatre.
"At this point they didn't really care who on the show saw them as they walked along the street arm-in-arm," the source added. "We were quite shocked they were being so open about it but no one was surprised to find out they'd finally got it together.
"Sam then waved goodbye to everyone and led Chloe out of the bar and back to the hotel. They then walked off down the street arm-in-arm, with Chloe resting her head on his chest. It was really sweet."
They apparently spent the night together in Attwater's hotel room following further rehearsals on Friday.
Madeley, who has been linked to a presenting role on This Morning, wrote on Twitter: "Absolutely Lovin this tour so far! Everyone is wicked and I'm enjoying spending time with everyone. X (sic)."
Attwater recently admitted that his Dancing On Ice win hadn't yet sunk in.