Praise be to Allah.
We put the following question to Shaykh Muhammad ibn Saalih al-‘Uthaymeen, may Allaah preserve him:
Has a man agreed to divorce his wife or has he already divorced her, if what he said was: “I agree to divorce my wife and she is now to be considered divorced”?
This is a divorce, and if she has completed her ‘iddah (waiting period of three menstrual cycles following divorce) then she is free to marry someone else. But if they have children together, I advise him to go back to her. He has the right to take her back so long as he issued just one divorce. And Allaah knows best.