Hmm, hard to say though. The bible never states explicitly that they are completely immortal, or actually alive for that matter. I would imagine god should have the ability to destroy them.
These passages should show that they were created by God and are immortal.
Nehemiah 9:6King James Version (KJV)
6 Thou, even thou, art Lord alone; thou hast made heaven, the heaven of heavens, with all their host, the earth, and all things that are therein, the seas, and all that is therein, and thou preservest them all; and the host of heaven worshippeth thee.
Colossians 1:16King James Version (KJV)
16 For by him were all things created, that are in heaven, and that are in earth, visible and invisible, whether they be thrones, or dominions, or principalities, or powers: all things were created by him, and for him:
Psalm 148:2-5King James Version (KJV)
2 Praise ye him, all his angels: praise ye him, all his hosts.
3 Praise ye him, sun and moon: praise him, all ye stars of light.
4 Praise him, ye heavens of heavens, and ye waters that be above the heavens.
5 Let them praise the name of the Lord: for he commanded, and they were created.
Luke 20:35-36King James Version (KJV)
35 But they which shall be accounted worthy to obtain that world, and the resurrection from the dead, neither marry, nor are given in marriage:
36 Neither can they die any more: for they are equal unto the angels; and are the children of God, being the children of the resurrection.