The charity, which aims to end violence against women and girls, will hold an auction throughout the rest of November through to early December to raise funds to support their work.
The auction will release signed handwritten lyrics to the highest bidder, or to prize winners in a $10 entry sweepstake prize draw.
Eilish has contributed signed lyrics to “Your Power,” while Keys has given “Fallin,” Carlile’s donated “Right on Time,” and Kidjo’s gifted “Agolo”.
“I have long believed that music can build bridges and bring people together,” Lennox said in a statement.
“It is wonderful to see these phenomenal female artists stand side by side with women and girls around the world facing and fighting gender-based violence,” she added.
According to The Circle, all proceeds from the lyrics will go towards supporting women and girls internationally who have experienced domestic abuse or violence.
The support services offeed include counselling, safe houses and accommodation, coaching, education, and legal advice for those that have been affected.
The charity was formed in 2008 by Lennox and “brings Global Feminists together to fight for a fairer world for women and girls across the world”.
It has now grown into an “independent movement of women and allies from all walks of life who are bonded by the desire to live in a world where women and girls have equal rights and equal opportunities”.
The auction will be held between Tuesday 22 November and will end at 11.59 GMT on 5 December.
The sweepstakes entries for prizes will close on 15 December at 11:59 GMT.