TECHNICALLY speaking, and only for historical, rather than biblical info, we know that the Roman Legions and a Roman Governor were in charge of that entire region. The agitation of the common people by the Pharasees and Hebrew temple 'priests' were the catalyst in causing the Roman Governor to make the decision that he made to have Christ excecuted.
We also know, BIBLICALLY, that King David wrote about these happenings in prophesy 1000 years before they actually took place. Compare the words in the Old Testament Psalm 22 (KJV) with the text as found in the New Testament - Matthew 27-28 (KJV), Mark 15 (KJV), Luke 23 (KJV) right down to King David's prophesy about the Roman Soldiers casting lots for Christ's clothing.
This excecution was all part of God's plan to allow MAN to be saved if MAN wanted to be saved, through the belief in Christ as the Savior and through His blood being shed for our sins.