The letter to the Ephesians starts this way  1:1, "Paul, an apostle of Jesus Christ by the will of God..."

When someone wrote a letter back then, they reversed the order that we use today.  Instead of starting with the name of the people you were writing to, you stated who you were.  (Today, we would give our name at the end of the letter.)  However, the letter to the Ephesians starts with, "Paul."

Not only did Paul want them to know his name, but also his standing.  He was an Apostle of Jesus Christ.  There had been 12 Apostles.  But Judas was dead.  So Matthias had been chosen by the other eleven to fill his place.  Problem is, Matthias was chosen by "lot," (kind of like tossing a coin for heads or tails).  Matthias wasn't "called."  Christ didn't tell them to replace Judas.  If Jesus had wanted Judas replaced, He had plenty of time after the resurrection to do that.  So what happened?

Jesus had appeared to the disciples before he left them--to be taken up into heaven.  Jesus told all of them to 1. Go to Jerusalem and 2. Wait for the Holy Spirit.  Which they got "half" right.  They left the Mount of Olives and returned to Jerusalem.  But Peter, who was never much good at waiting, decided they needed to have an election--while they were sitting around waiting on the Holy Spirit.  Oops.

He told the group that since Judas was dead, they needed to replace him.  And the replacement needed to be someone who had accompanied them during:  "...the time that Jesus went in and out among us...beginning from the baptism of John unto that day he was taken up from us...a witness with us of his resurrection." Acts 1:15-26  Any number of men fit Peter's description.  

Peter's heart was in the right place.  He made a list of qualifications for the job of Apostle.  He was ready to get started doing the work of the Lord.  But like you and me, sometimes we ask God to bless what we have already done--without asking Him if He wanted us to do that thing in the first place.

They chose two men, Justus and Matthias, cast lots, and Matthias was chosen.  He was a good man I am sure.  But you never hear of him again.  So when Paul wrote to the Ephesians, he wanted them to be sure and know his standing.  It was by, "...the will of God."  Nobody cast lots to elect Paul as an Apostle.  Paul was God's man for the job.  Called.  (Paul would not have qualified for Peter's list.)