Roma have appointed Vincenzo Montella as his replacement.
"I hope that Vincenzo Montella and my lads can keep the Roma flag flying high, always and everywhere," Ranieri said.
"In these hours, many people have sent messages of faith and support to me, people from the footballing world and non.
"I thank everyone, in particular President Rosella Sensi for her kind words and for the opportunity to Coach the team of my heart.
"I once again thank the team for our journey together and for the success which we have shared with everyone at Trigoria.
"I would also like to thank the fans who, in a delicate moment of my sporting and Romanista life, paid attention to me."