Paul, an apostle of Jesus Christ, - See the notes at Romans 1:1.
By the will of God - Called to be an apostle in accordance with the divine will and purpose; see the notes at Galatians 1:1.
According to the promise of life which is in Christ Jesus - In accordance with the great promise of eternal life through the Saviour; that is, he was called to be an apostle to carry out the great purpose of human salvation; compare Ephesians 3:6. God has made a promise of life to mankind through faith in the Lord Jesus, and it was with reference to this that he was called to the apostleship.