The first disciple to whom Jesus addressed the words "Follow me" was Philip. Philip was from the same city as Andrew and Peter: Bethsaida (see John 1:44). But Andrew had followed Jesus the day before, of his own accord, not waiting to be called. The Bible says that two of John's disciples had followed Jesus together, and identifies one of these as being Andrew. So Andrew was one of the first two.
Can we figure out who the other one of the "first" disciples was? Let's try.
The First Two Disciples: Andrew and ?
One of the two which heard John speak, and followed him, was Andrew,
Simon Peter's brother. (John 1:40, KJV)
The Third Disciple: Simon Peter
He first findeth his own brother Simon, and saith unto him, We have
found the Messias, which is, being interpreted, the Christ. And he
brought him to Jesus. And when Jesus beheld him, he said, Thou art
Simon the son of Jona: thou shalt be called Cephas, which is by
interpretation, A stone. (John 1:41-42, KJV)
The Fourth Disciple, First One to Be Called by Jesus: Philip
The day following Jesus would go forth into Galilee, and findeth
Philip, and saith unto him, Follow me. (John 1:43, KJV)
The Fifth Disciple: Nathanael
Philip findeth Nathanael, and saith unto him, We have found him, of
whom Moses in the law, and the prophets, did write, Jesus of Nazareth,
the son of Joseph. ... Nathanael saith unto him, Whence knowest thou me? Jesus answered and said unto him, Before that Philip called thee, when thou wast under the fig tree, I saw thee. (John 1:45,48; KJV)
We see no more of the disciples' callings in John's account, for the next we know from John is that Jesus has 12 disciples already.
Then said Jesus unto the twelve, Will ye also go away? (John 6:67,
The other three gospels give account of Matthew's calling.
Matthew / Levi Matthew
And as Jesus passed forth from thence, he saw a man, named Matthew,
sitting at the receipt of custom: and he saith unto him, Follow me.
And he arose, and followed him. (Matthew 9:9, KJV)
And as he passed by, he saw Levi the son of Alphaeus sitting at the
receipt of custom, and said unto him, Follow me. And he arose and
followed him. (Mark 2:14, KJV)
And after these things he went forth, and saw a publican, named Levi,
sitting at the receipt of custom: and he said unto him, Follow me.
(Luke 5:27, KJV)
Judas, we know, was not called by Jesus, but was suggested to him by the other disciples, and Jesus accepted him. None of the other disciples is directly mentioned as to having been called, with the exception that several of them, including Andrew who had followed Jesus without being called, were later called, as if to make it "official."
And Jesus, walking by the sea of Galilee, saw two brethren, Simon
called Peter, and Andrew his brother, casting a net into the sea: for
they were fishers. And he saith unto them, Follow me, and I will make
you fishers of men. (Matthew 4:18-19, KJV)
And going on from thence, he saw other two brethren, James the son of
Zebedee, and John his brother, in a ship with Zebedee their father,
mending their nets; and he called them. (Matthew 4:21, KJV)
Because these callings were early in the process, and should have preceded even Levi Matthew, we can infer that either James or John must have been the "other disciple" who had first followed Jesus. John, who is the one to have recorded Andrew following Jesus, would have had little reason to hide his brother's identity, had it been James; but both modesty and the fact that John seems to have had personal knowledge of Andrew's following of Jesus imply that the other disciple was none other than John.
Andrew and John were Jesus' first disciples, both following him together after the testimony of John the Baptist had identified Jesus.