When and who was the first disciple to truly believe Jesus' claims Same as title, the question came up in bible study looking for more information.
The phrasing of the question is a bit tricky because it assumes the first believer was a disciple.  It may also assume a certain gender.  So I have provided three answers, but in the apparent order of actual belief.  First are some guards at the tomb.  Second is Mary Magdalene and probably the other women.  Third is the male disciples.
FIRST GUARDS
If we look at the resurrection account in Matthew 28, we find that the first believers (Jesus is the Messiah, crucified, buried, resurrected) were the guards at the tomb.

And for fear of him [the Risen Lord] the keepers did shake, and became as dead men. Mat 28:4

The guards were certainly instructed about the circumstances of their watch.  A crucified man has been entombed, but some of his followers think he will rise from the dead alive on the third day.  They think he is the King of the Jews, the prophesied Messiah.  Watch carefully.
So when it happens as they were told, we read later in the chapter that only some of the guard go tell the chief priests.

Now when they were going, behold, some of the watch came into the city, and shewed unto the chief priests all the things that were done.  Mat 28:11

Why some?  Why not all?  Because it would be evident that the others ended up believing.  The guards were not disciples, but I think a solid case can be made that some of the guards were the first believers.
SECOND WOMEN
What about actual disciples?  Do women count as disciples?  If so, then the next case would be Mary Magdalene.  She comes to the sepulchre to annoint Christ, but find his body gone.  She tells Peter and John who come see the body is indeed missing, but they don't believe in the resurrection at that time.

The first day of the week cometh Mary Magdalene early, when it was yet dark, unto the sepulchre, and seeth the stone taken away from the sepulchre. Then she runneth, and cometh to Simon Peter, and to the other disciple, whom Jesus loved, and saith unto them, They have taken away the Lord out of the sepulchre, and we know not where they have laid him.  John 20:1-2
Then went in also that other disciple, which came first to the sepulchre, and he saw, and believed. John 20:8

Believed what?  Believe the idea that the body had been stolen.

For as yet they knew not the scripture, that he must rise again from the dead. John 20:9

They depart, but Mary stays.

Jesus saith unto her, Touch me not; for I am not yet ascended to my Father: but go to my brethren, and say unto them, I ascend unto my Father, and your Father; and to my God, and your God. John 20:17

She tells the other disciples, but they are still in a state of denial.
THIRD MALE DISCIPLES
If one is asking about the first male disciple to believe that Jesus is Messiah, then we look at Luke 24 and the two travelers to Emmaus.  Unbeknown to them, it is Jesus who is explaining the scriptures to them, concluding with this question.

Ought not Christ to have suffered these things, and to enter into his glory?  Luke 24:26

But not until the breaking of bread was revelation given.

And it came to pass, as he sat at meat with them, he took bread, and blessed it, and brake, and gave to them. And their eyes were opened, and they knew him; and he vanished out of their sight. Luke 24:30-31