Vejvoda was born and died in Prague-Zbraslav. From 1936 to 1960, he lived in Vrané nad Vltavou, after he married the local native Božena Zamrazilová.
He learned to play the fiddle and flugelhorn in a band led by his father. Later he played these instruments in a military band. He started to compose in the 1920s while he worked as a bartender in a pub owned by his father-in-law. In 1929 he wrote the Modřanská polka named after Modřany, a suburb of Prague where it was played the first time.