Well for Biblical verses on theosis see I Cor 15:35+ which is one of the clearest biblical descriptions, and also I John 3:2, which is the most basic and clear statement explaining it. One way to look at it is that theosis is just a fancy name for our inheritance in the resurrected, and transformed nature of the Incarnate Christ. To some extent that starts now for us, in a mirror darkly, but will be completed for us and all of creation at the final restoration of all things. cf Rom 8:18-23, 29-30
as Hyppolytus says, God the father sent His Son to man, " in order to wash him with water and the Spirit; and He, begetting us again to incorruption of soul and body, breathed into us the breath of life, and endowed us with an incorruptible panoply. If therefore, man has become immortal, he will also be god, and if he is made god by water and the Holy Spirit after the regeneration of the laver, he is found to be also joint-heir with Christ after the resurrection of the dead." Discourse on Holy Theophany
And St John Chrysostom, commenting on Gal 3:27 and Paul's statement that in our baptism we put on Christ. "Why does he (Paul) not say ' for as many of you as have been baptized into Christ, have been born of God', for this was what directly constituted proof that they were sons? The reason is that he states it in a much more awe-inspiring way.: if Christ be the Son of God and you have put him on, you, by having the Son within yourself and being fashioned after his pattern, have been brought into one kindred and nature with him.."