Per Teodor Cleve (10 February 1840 – 18 June 1905) was a Swedish chemist and geologist.
After graduating from the Stockholm Gymnasium in 1858, Cleve matriculated at Uppsala University in May 1858, where he received his PhD in 1863. After employment with the university in Uppsala and travels in Europe and North America, he received a professorship of general and agricultural chemistry in Uppsala in 1874. He was elected a member of the Royal Swedish Academy of Sciences in 1871 and he received the Davy Medal of the Royal Society in 1894, "for his researches on the chemistry of the rare earths". The mineral cleveite was named in 1878 by the geologist and explorer Adolf Erik Nordenskiöld in his honour. Cleve was the father of the botanist and chemist Astrid Cleve and the grandfather of her son, Ulf von Euler, a Nobel prize winner, physiologist and pharmacologist.
In 1874, he concluded that didymium was in fact two elements, now known as neodymium and praseodymium. He also discovered the elements holmium and thulium in 1879.