His musical training took place in Dresden (as a chorister at the Saxony Court (under the direction of Heinrich Schütz), then in Hamburg where he worked with the famous Saint Peter's church (Petrikirche) organist Jacob Schultze Praetorius.

He was introduced to the italian style - because Schütz had journeyed in Italy when a young man and he had met Gabrieli and Monteverdi - as well as the style of Sweelincks pupils, who had settled in Hamburg. He travelled to Denmark in 1637 with Schütz, became organist in Dresden at the Electoral Court of Saxony from 1638 to 1642, and returned to Denmark until 1637 (during the Thirty Years War).

During a new (and his last) stay in Dresden from 1649 to 1655, he met Johann Jakob Froberger during a musical competition which had been organized by the Elector. They remained friends and in correspondence with each other since then. In 1655, after a competition, he was named titular organist at Saint James church (Jakobkirche) in Hamburg and then, he spent all his remaining life in this town. There he founded a renowned orchestral ensemble, the so-called Collegium Musicum.

Weckmann composed, for the organ choral variations and preludes, for the harpsichord pieces that mix italian and french influences, various sonatas for 3 and 4 instruments as well as orchestral and vocal sacred music.