The German-Iranian, who won the European under-21 title with Germany last year, opted for Iran following lengthy talks with Iran coach Afshin Ghotbi, the Teheran sports newspaper Khabar Varzeshi reported.
The report said Dejagah, an attacking midfielder who can also play as a striker, would be given the number 10 shirt which was worn for more than 10 years by Ali Daei, a footballing legend in Iran.
There was no official confirmation for the report.
Iran is preparing for the 2011 Asian Cup which begins in Qatar on January 7. Dejagah, 24, would be eligible to join the Iran squad as he has not been capped at senior level by Germany.