Częstochowa, Iverion and Vladimir Icons are said to have been panted by him.
Also the Tikhvin: http://ocafs.oca.org/FeastSaintsLife.asp?FSID=101821
The form of icon where the Theotokos gestures toward her Son (called "the Directress") is a form first painted by St Luke.
You can see on the Vladamir icon that there has been extensive repainting done to the icon, and that the faces of the Mother of God and Christ seem "pasted on". However, it is the faces on the icon which have survived, whilst the rest has been repainted over time. Even those who don't believe that the Vladimir icon dates back to St Luke agree that the faces are the original part of the icon.
As for how it came to pass --- St Luke's Gospel has the greatest amount of all the Gospels written about the Theotokos, including the most complete narrative (in the NT) of the annunciation and the birth of Christ. It is believed St Luke could write this, and also paint icons of the Mother of God, because he knew her personally.
Mosaic of St Luke painting, then having the icons approved by, the Mother of God:http://iconreader.files.wordpress.com/2011/11/st-luke-paints-theotokos-who-blesses-icons-6.jpg