Does he have to refrain from eating on the day he becomes Muslim?

Yes, he has to refrain from eating for the rest of the day on
which he becomes Muslim, because he is now one of the people who are under
this obligation. This is different from the case when an impediment to
fasting ceases to apply; when an impediment to fasting ceases to apply, the
person does not have to refrain from eating for the rest of that day, for
example, if a woman’s period ends during the day and she becomes pure, she
does not have to refrain from eating for the rest of the day. Similarly if a
sick person who didn’t fast because of sickness recovers during the day, he
does not have to refrain from eating, because it was permissible for him not
to fast on this day, even though he is one of those who come under this
obligation – i.e., a Muslim. This is different from the case of one who
becomes Muslim during the day; he has to refrain from eating but he does not
have to make up that day. But those people – menstruating women, people who
are sick and so on, do not have to refrain from eating but they do have to
make up that day. End quote. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him).