Some inferences can be drawn from scripture, particularly from 1 Corinthians 15:
But Christ has indeed been raised from the dead, the firstfruits of those who have fallen asleep. (v14 NIV)
This indicates to us that Christ's resurrection should be viewed in a different manner than previous examples of people being raised from the dead (Lazarus, Widow of Nain's son etc.) - which would perhaps be better termed resuscitations as their bodies were not substantially changed and would have been subject to aging and (re-?)death.
Later in the chapter, the nature of resurrection for all believers is discussed. As Christ is the firstfruits, what applies in a believer's resurrection would most likely have been what happened to Jesus (at least in part - due to Him being the divine Son of God and triumphing over the powers of death and hell by His work on the cross there would certainly have been some circumstances unique to Himself):
But someone will ask, “How are the dead raised? With what kind of body will they come?” How foolish! What you sow does not come to life unless it dies. When you sow, you do not plant the body that will be, but just a seed, perhaps of wheat or of something else. But God gives it a body as he has determined, and to each kind of seed he gives its own body. Not all flesh is the same: People have one kind of flesh, animals have another, birds another and fish another. There are also heavenly bodies and there are earthly bodies; but the splendor of the heavenly bodies is one kind, and the splendor of the earthly bodies is another. The sun has one kind of splendor, the moon another and the stars another; and star differs from star in splendor. So will it be with the resurrection of the dead. The body that is sown is perishable, it is raised imperishable; it is sown in dishonor, it is raised in glory; it is sown in weakness, it is raised in power; it is sown a natural body, it is raised a spiritual body. If there is a natural body, there is also a spiritual body. So it is written: “The first man Adam became a living being”; the last Adam, a life-giving spirit. The spiritual did not come first, but the natural, and after that the spiritual. The first man was of the dust of the earth; the second man is of heaven. As was the earthly man, so are those who are of the earth; and as is the heavenly man, so also are those who are of heaven. And just as we have borne the image of the earthly man, so shall we bear the image of the heavenly man. I declare to you, brothers and sisters, that flesh and blood cannot inherit the kingdom of God, nor does the perishable inherit the imperishable. Listen, I tell you a mystery: We will not all sleep, but we will all be changed— in a flash, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, the dead will be raised imperishable, and we will be changed. For the perishable must clothe itself with the imperishable, and the mortal with immortality. When the perishable has been clothed with the imperishable, and the mortal with immortality, then the saying that is written will come true: “Death has been swallowed up in victory.” “Where, O death, is your victory? Where, O death, is your sting?” (vv35-55 NIV)
In summary, His physical body would have been transformed to a glorious, imperishable, immortal spiritual body that has some essence in common with the previous form, but is a greater manifestation of that essence in a way that is like a seed of a plant becoming the mature plant. From other places in scripture we know that He could ascend with this body to the Father, be translated from place to place including through solid walls and yet was tactile and able to consume normal food.