Sir Charles began collecting paintings around 1880, starting mostly with 19th-century landscapes and 18th c. portraits. The Tennant family fortune began with Charles' grandfather, who invented bleaching powder and established a huge and successful chemical works in Glascow. Sir Charles' father, John, expanded the business and became a leading Glascow philanthropist. At age fourteen, Sir Charles went to work in business at Liverpool. He made his own first fortune by his early twenties, buying railroad stock. In 1849, at age twenty-six, he married Emma Winsloe (1821-1895) and moved the next year to London. There he profited greatly from the industrial revolution.
He began forming his personal library early on, having many volumes rebound in Moroccan leather according to current fashion, and started collecting mezzotints of 18th c. English portraits in the 1870's through London print dealer Francis Harvey. In 1880 Tennant became associated with William Agnew, of the well-known London art firm Thomas Agnew & Sons, who purchased many paintings for him in the ensuing years. Sir Charles also commissioned several portraits of his family members, and was himself an elegant subject. One of the most appealing portraits of Tennant is that by John Singer Sargent, painted in 1901.
Tennant served as the local Justice of the Peace and Deputy Lieutenant, and was a Member of Parliament for Glasgow (1879-1880) and for Peebles and Selkirk (1880-1886). He gave several paintings to the Glasgow Museum and Art Gallery, and lent generously of his collection to various exhibitions. In 1893 and 1894, he served as a trustee of the National Portrait Gallery; from 1894 until his death in 1906, he was a trustee of the National Gallery in London. He had thirteen children with his first wife Emma, of whom three sons died young. He married secondly in 1898 to the much younger Marguerite Agaranthe Miles (1868-1943), having with her four daughters (one died early).