The band's record label announced earlier this evening that she had left the group and would be replaced by Eurovision star Jade Ewen.
Buchanan wrote: "I've had a great time and have achieved more than I ever thought I would.
"Although it was not my choice to leave, it's time to enter a new chapter in my life. I have nothing but positive things to say about the girls and I wish them the best of luck. I would like to state that there were no arguments, bullying or anything of the sort that led to this.
"Sometimes a break down in communication and lack of trust can result in many different things. I would also like to point out that I have always supported the girls and they have also supported me."
She added: "I want to thank the Sugababes fans and my fans for all your support and all who have never judged me, but accepted me for who I am... The feisty, funny, professional, fearless motor mouth. This is not the end... but the beginning!"
Buchanan also admitted that she is "nervous" and "excited" about embarking on a career as a solo artist and is planning to "take some time to focus on me".