The split is the second to hit the stars of the current series, and follows comedian Seann Walsh being dumped by his girlfriend Rebecca Humphries after he was pictured kissing dance partner Katya Jones.
Professional dancer Buswell, who is partnered with YouTube star Joe Sugg, had been dating Quinlan for around 10 months.
A representative for Buswell said: “Due to their busy schedules and distance they have split, but still remain really close friends.”
According to The Sun, the split was prompted by concerns over Buswell’s working relationship with Sugg.
A Strictly source was quoted in the newspaper as saying: “Everyone on set’s been discussing how close they’d become. It did not go unnoticed by Anthony.”
Buswell, 29, and Sugg, 27, are among the bookies’ favourites to win this year’s series.
This weekend, they will dance a waltz to The Rainbow Connection by Sleeping At Last.
Last week, Walsh and Jones were the focus of attention after being pictured kissing despite both already being in relationships - Walsh with now ex-partner Humphries, and Jones with fellow Strictly professional Neil Jones.
They both apologised for their actions.
The pair faced the music on the dancefloor in Saturday’s episode and despite speculation from fans that they may be booted off the show, they won approval from viewers to return again this weekend.Join our Facebook group Our Edinburgh to share images and news from and around the Capital