Can Yücel was the son of a former Minister of National Education, Hasan Ali Yücel who left his mark on the history of education in Turkey, and a grandchild of an Ottoman sea captain who perished with the frigate Ertuğrul. He studied Latin and Ancient Greek at Ankara University and Cambridge. He later worked as a translator at several embassies and in the Turkish language section of the BBC in London. After his return to Turkey in 1958, he briefly worked as a tourist guide in Bodrum and Marmaris, and then lived in Istanbul where he worked as a freelance translator and started writing poetry.
In his later years, he settled in the remote peninsular town of Datça in southwestern Turkey where he died of throat cancer. His tomb is much visited. He had two daughters, Güzel and Su, and a son, Hasan, from his marriage to Güler Yücel.
Can Yücel was known for using slang and vulgar language in his poems. However, even his critics agreed that his skill in using words in a simple and understandable way is worthy of praise and appreciation. The main themes and inspirational sources in his poems are nature, people, events, concepts, excitements, perceptions, and emotions. His family was of utmost importance to him and his loved ones are mentioned in many of his poems, such as "To my Little Daughter Su," "To Güzel," and "I Loved My Father the Most in Life."