Matthew states that Judas hanged himself. I've always wondered about this contradiction.
Here's a helpful post that helps us reconcile the two gospel accounts of Judas' death.
Is it possible, that Jesus picked Judas, to be the one to betray him, by giving him the bread???
As I said in the sermon, we focus more on the choice (either Judas' choice or, as you're asking, "Did Jesus choose Judas?"). The focus of Scripture is that Judas' actions were fulfillment of Scripture. In the gospels, you can almost feel Jesus' sorrow towards Judas because of what He knows Judas is going to do. He loved all of the disciples even while knowing that they would betray and abandon Him while He was arrested and crucified. Thus, I wouldn't confuse Jesus giving Judas the bread with Jesus choosing Judas to be His betrayer.