A son of a miller, at eleven years of age, he became a student at Leipzig, Saxony university. Three years later he continued his studies at the Alma Mater Rudolfina in Vienna, Austria. There he became a pupil and friend of Georg von Peurbach. In 1457 he graduated with the degree "magister artium" and held lectures in optics and antique literature. In the same year he built an astrolabium for Maximilian I, in 1465 a portable sundial for pope Paul II. The work with Peurbach brought him to the writings of Nikolaus von Kues (or Cusanus) who had a heliocentric approach. However, Regiomontanus remains geocentric following Ptolemy's work. After Peurbach has died he continued his translation of Ptolemy's Almagest which was initiated by Bessarion. From 1461-65 Johannes Müller or Regiomontanus lived and worked at Cardinal Bessarion's house in Rome. He writes De Triangulis omnimodus (1464) and Epytoma in almagesti ptolemei. De Triangulis was one of the first textbooks, presenting the current state of trigonometry including a kind of repetitorium (list question for recapitulating each chapter). In the Epytoma he commented the translation and indicated inaccuracies. Later, Nicolaus Copernicus will refer to this book as having influenced him much. In 1467, he went from Rome to work at the court of Matthias I, King of Hungary. He calculated and made extensive astronomical tables. He also built astronomical instruments.
In 1471 Johannes Müller moved to the Free City of Nuremberg in Franconia, which at that time was one of the most important places of learning, publication, commerce, artistry etc of the empire. Regiomontanus remains known for building the first Astronomical observatory of Germany, perhaps of Europe, at Nuremberg. He made and printed many astronomical charts.
1475 he went and worked with pope Sixtus IV in Rome on Calendar Reform. While in Rome, Müller died mysteriously; some say of the plague, others (more feasibly) of assassination. It was July 6, 1476, and he had just turned forty exactly one month earlier.
Johannes Müller was internationally famous already during his lifetime. He was a very active writer. Despite his plans for writing four times the volume he actually did get to finish, he left us a number of works.
It is not true that after his death he simply became known for the place of his birth, Königsberg or in Latin: Regiomontanus. In fact, the story is much more interesting: It happens that in the time of Müller it was common for scholars to author their works under Latin pennames. Copernicus did likewise and that is why we do not know him as Zepernik, as he was really called. By the same token, the only reason we know Regiomontanus by this place-name is that we can only know him, as is true for everyone sooner or later, by the very words he wrote.