The Saturdays star Bridge praised Nelson during an appearance on the BBC's Morning Live programme as she also revealed that the move had made her "really sad".
The singer said in a statement: "The truth is recently being in the band has really taken a toll on my mental health".
Nelson began her note by listing the various accomplishments Little Mix was able to achieve since its inception on The X Factor singing competition show, including selling out the 20,000-capacity O2 Arena in London and winning awards - and thanking their fans for making it all possible.
'I think they've had such a successful career and they're obviously all really close and I feel like the girls clearly support her decision, but it must have been really hard for them all.
She added: "Making friends and fans all over the world, I can't thank you all enough from the bottom of my heart for making me feel like the luckiest girl in the world".
'Also if you've never had one before, it's so hard to understand.so I did realise it might be a good thing for those people to see what it's like'.
"I need to spend some time with the people I love, doing things that make me happy", she wrote.
The official Little Mix Instagram account has also released an emotional statement which reads: "After an wonderful 9 years together Jesy has made the decision to leave Little Mix".
'There are probably lots of people before her that weren't fearless enough to do that and I think she's setting a really good example to all the young fans that love Little Mix already to say, "success is awesome but your health and wellbeing has to be at the forefront"'. I want to say thank you to everyone involved in our journey.
The news comes a day after Little Mix performed as a trio on British TV show Strictly Come Dancing and weeks after a representative for the band confirmed Jesy would be taking an "extended break" due to "private medical reasons". "I always get told I look ugly or fat or whatever else", she said. "We love her very much and agree that it is so important that she does what is right for her mental health and well-being", the joint message read. "I hope that you'll continue to fulfill all of your dreams and keep on making music that people love".
U.S. fan Sabian Lucas says Jesy's Odd One Out documentary on BBC Three "made waves and inspired people across the world of all ages".
"We are still very much enjoying our Little Mix journey and the 3 of us are not ready for it to be over".