Veit was born in Berlin. He received his first art education in Dresden and Vienna. He was strongly influenced by, and joined, the Nazarenes in Rome, where he worked for some years before moving to Frankfurt.
In Frankfurt, where his most important works are preserved at the Staedel Institute, he was active from 1830 to 1843 as director of the art collections and as professor of painting. From 1853 till his death in 1877 he held the post of director of the municipal gallery at Mayence. Like his fellow Nazarenes he was more draughtsman than painter, and though his sense of colour was stronger than that of Overbeck or Cornelius, his works are generally more of the nature of coloured cartoons than of paintings in the modern sense.
Veit's principal work is the large fresco of "The Introduction of Christianity into Germany by St Boniface", at the Staedel Institute in Frankfurt. In the cathedral of that city is his "Assumption", whilst the Berlin National Gallery has his painting of "The Two Marys at the Sepulchre". To Veit is due the credit of having been the first to revive the almost forgotten technique of fresco painting.