For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
It depends on the reason for his divorce. If it was for his wife's unfaithfulness, then she separated from him and not he from her, so his remarriage would not fall under 'adultery.' If it was for any other trifling reason, then technically he would be committing adultery. I don't think she would be classified as committing adultery since a married woman can't commit adultery with her first husband.
We are not under the law, however, but we are under grace. We can still learn a lot from this principle - as Jesus is teaching what is good and what is not good to do here. However, we also have the forgiveness of Christ and the teaching of the Holy Spirit.
All the parties in such a case should seek prayer and counsel with God and other accountability partners within the church. Reconciliation with his first wife would be the ideal, but in some cases that is impossible.
The short answer is ,”Yes”. Any man or woman that has never married that decide to do so to a person who has been married before them is committing adultery.
For any of you young men and women who have never wed another and who may also be pure, seek God’s counsel in this matter because it is on subject He takes seriously. I am a Christian counselor and I have had couples come to me asking about remarriage because they have reconciled with one another, matured in Christ, and come to find they still hold love in their hearts for one another. I have had many become furious and storm out and some that just break down and weep. Hearing Gods Word on the remarriage of an original couple after divorce is very hard. If one or both has remarried during the time of separation they can not wedd with one another again if they do God says it plainly that both are committing adultery and would be living in perpetual sin. It breaks my heart to see that their original love has matured and surfaced and they wish to remarry but by Gods Word can not. It is not to say that they can not love one another and care for one another they just may never again share the marriage bed together and having gone through this myself I understand how important that part is but forgiveness and love are more so. Sex for personal gratification is a sin and there are so many today that refuse to see that. I pray God will lead you to an answer.
On the subject of a married woman can not commit adultery with her first husband I can only say what God’s Word says and He makes it clear.
If a man and woman are married for the first time and for whatever reason decide they just can not endure one another and divorce. Now being divorced if either marrys another besides their original spouse they commit adultery. If they decide to reconcile with their original spouse, in this case it would be the wife who has remarried and wants to go back to her first husband, divorces her second to return to her first she will be committing adultery and what’s worse is if her first remained celibate she will cause him to commit adultery as well. Then they will both be living in perpetual sin.
The original couple can re-wed even if the wife committed adultery through remarriage or regular adultery, though it is considered that the woman has cast a terrible shame upon the husband. (There is an OT law prohibition against a man who *initiates* the divorce against a non-adulterous wife from remarrying her though, as that is a disgrace to him.)
God makes this point in Hosea (the whole book) where he commands Hosea to marry a prostitute. She leaves him to return to her adulterous life. God then commands Hosea to take her back. This was all to have a physical prophetic parallel that God would take back adulterous Israel. Since God does not command people to sin nor does He lump Himself in with sinners, this can't be a sin.
God also makes this point in Jeremiah 3. He compares Judah to a former wife committing lewd adultery, but promises to take her back. Jer 3:14 sums this up: "“Return, faithless people,” declares the Lord, “for I am your husband. I will choose you—one from a town and two from a clan—and bring you to Zion." God didn't divorce Israel and Judah - they were first unfaithful. (Isa 50:1)
As for a wife returning to her former husband, this also happened in the case of Michal.