It is not show exactly when Ensign Chekov joins the crew of the Enterprise during The Original Series. However, because Khan said "I never forget a face... Mr. Chekov isn't it?" we can assume it was before the episode Space Seed. Please see the question Khan & Chekov for further insights on this theory.
The Movie version of Chekov played by Anton Yelchin, came aboard Enterprise at the same time as everyone else.