All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
If the marriage contract was conducted with the consent of the bride's Wali (matrimonial guardian) and in the presence of witnesses, it is valid under Sharee‘ah whether it is registered officially or not. Please refer to Fatwa 83629 about the due conditions to the validity of marriage contract.
It should be highlighted that the separation between the spouses – even if for a long period of time – does not mean that divorce has taken effect. Separation has absolutely no effect on the marriage bond as underlined in Fataawa 89825 and 82732.
In any case, we advise you to seek reconciliation with your wife; verily, this is better. Divorce often causes great harm to the children. However, if there is no room for reconciliation, you can opt for divorce. It is not right for you to leave the matter "hanging", so that the wife is [effectively] neither divorced nor married.
Allaah Knows best.