Förster studied music under his father Kaspar (1574-1652) and then under Marco Scacchi in Warsaw.
He sang bass and conducted choirs at the Polish court in Warsaw from 1638 to about 1643, then served as kapellmeister to Frederik III of Denmark in Copenhagen between 1652 and 1655.
In 1655, a war broke out between Denmark and Sweden, and Förster returned to Danzig, working as cantor at the Marienkirche there.
Förster's surviving works are mostly sacred cantatas for three voices, with two violins and continuo.
His other works include two oratorios, six trio sonatas, and four secular cantatas.