Praise be to Allaah.
There is no tashahhud after sujood al-sahw, because the Messenger of Allaah (peace and blessings of Allaah be upon him) did not do that, as is indicated by the saheeh ahaadeeth (see question # 211). If he had done that, he would have taught it to his companions would have said so, and they would have narrated it to others. And he (peace and blessings of Allaah be upon him) said: “Pray as you have seen me praying.”
Shaykh Ibn Qudaamah said:
“Ibn Seereen and Ibn al-Mundhir said (concerning sujood al-sahw): there is tasleem [saying salaam] in them but there is no tashahhud.
Ibn al-Mundhir said: the tasleem [in sujood al-sahw] is proven from more than one isnaad, but there is some dispute concerning the tashahhud.”
(al-Mughni, 2/431, 432)
According to al-Nawawi, among the things we learn from the hadeeth of Dhoo’l-Yadayn are:
That sujood al-Sahw was done at the time of the Prophet (peace and blessings of Allaah be upon him).
That it consists of two prostrations, and that one should say Takbeer (“Allaahu akbar”) for each prostration. They are like the prostrations of prayer, because they are called sujood, and if they had been different, he would have explained that. One should say salaam after doing sujood al-sahw, but there is no tashahhud, and if one has to do sujood al-sahw because of doing something extra in the prayer, this should be done after the salaam.
(Sharh Muslim, 5/71).
And Allaah knows best.