From 1908 to 1912, he attended the Höhere Graphische Bundes-Lehr- und Versuchsanstalt, then studied at the Academy of Fine Arts with Alois Delug.
In 1910, Velim had already held his first official position as an assistant to Alfred Roller at the Erste Internationale Jagd-Ausstellung [de].
In 1930, he held his last exhibition with the Wiener Secession, and his works were part of the art competition at the 1936 Summer Olympics.
His personal life also went poorly, as his only son was killed in World War II, and his wife filed for a separation after over twenty years of marriage.
In Die Presse, the cause was given as a heart attack but other, international sources gave it as varnish poisoning.