The 55-year-old actor - husband of Hollywood star Dame Emma Thompson - landed in the bottom two after his Samba to the Macarena with partner Karen Hauer was branded "uncomfortable" and "awkward" to watch by the judges.
Wise said of leaving the competition: “I have had an amazing time, I feel unbelievably privileged so thank you all for having me."
He added: "The highlight undoubtedly was doing the week two Couple's Choice - the banging disco for my sister Clare."
Watch: Who is Strictly's Greg Wise?
The Sense and Sensibility actor previously revealed he signed up to take part in the celebrity dance show in memory of hid late sister, Clare, who died from cancer in 2016.
Wise landed in the dance off opposite comedian and TV presenter Love, 41, who had already been saved by the judges last week when she was placed in the bottom two with soap star Katie McGlynn.
This week Love performed a Waltz with partner Graziano Di Prima to Mariah Carey's Hero - which she dedicated to the memory of her late parents.
Both couples performed their routines again for the judges and Craig Revel Horwood chose to save Love and Di Prima.
He said: "The judges have been given this opportunity to save the better dancer and, for me, the better dancer tonight is Judi and Graziano.’
Motsi Mabuse also chose to save Love and Di Prima.
She said: "In the dance off I feel like both couples made mistakes and they were quite clear, but I feel that one couple recovered a little bit better with the situation. So I’m going to save Judi and Graziano."
Anton Du Beke chose to save Love and Di Prima - meaning they were immediately through to the next round with three votes.
Du Beke said: "I felt that the nerves got to both of the couples in the dance off, which is not surprising really, and they both made quite a lot of mistakes, but the couple who maintained an element of composure through the dance was slightly better and that would be Judi and Graziano."
Head judge Shirley Ballas - who would have had the deciding vote in the event of a tie - revealed, "Well I counted all the mistakes and from what I saw I would have saved Greg and Karen."
Wise's performance had been heavily criticised by the judges on Saturday's show, with Revel Horwood telling him: "It did look like you'd just come out of a double hip replacement operation. Very clumsy and technically quite bad."
Before the dance off Wise said: "I want to do the dance properly. I messed it up hugely."
He and Hauer performed a slow motion Macarena for their last dance as they bowed out of the contest.
The results show also saw Irish boyband Westlife perform their new single Starlight.
Westlife's Nicky Byrne competed in the show in 2012, dancing with Karen Hauer and got through to Week 10.
Webb underwent open heart surgery two years ago and his doctor has advised him not to continue with the competition as he began experiencing some worrying symptoms.
Ugo Monye and Oti Mabuse had to take the week off to allow Monye to recover from a back injury, but are expected to rejoin the remaining 10 couples on the dancefloor next when Strictly Come Dancing returns on Saturday 23rd October at 7:05pm.
Watch: Who's judging this year's Strictly?