The Matthew effect refers to the adage written some two-thousand years ago in the Gospel of St. Matthew: "For to all those who have, more will be given." Even two millennia later, this idiom is used by sociologists to qualitatively describe the dynamics of individual progress and the interplay between status and reward. Quantitative studies of professional careers are traditionally limited by the difficulty in measuring progress and the lack of data on individual careers. However, in some professions, there are well-defined metrics that quantify career longevity, success, and prowess, which together contribute to the overall success rating for an individual employee. Here we demonstrate testable evidence of the age-old Matthew "rich get richer" effect, wherein the longevity and past success of an individual lead to a cumulative advantage in further developing his or her career. We develop an exactly solvable stochastic career progress model that quantitatively incorporates the Matthew effect and validate our model predictions for several competitive professions. We test our model on the careers of 400,000 scientists using data from six high-impact journals and further confirm our findings by testing the model on the careers of more than 20,000 athletes in four sports leagues. Our model highlights the importance of early career development, showing that many careers are stunted by the relative disadvantage associated with inexperience.