The Hadith describe much excellence of Salaat Ut Tasbeeh. There is a Hadith in Sunan Ibn Majah:
Translation: It has been narrated on the authority of Hadhrat Abdullah bin Abbas (May Allah SWT be well pleased with them) that the Holy Prophet (Sallallahu alaihi wa sallam) told Hadhrat Abbas bin Abdul Muttalib (May Allah SWT be well pleased with them) that:
O Abbas! O My uncle! Should I not grant you? Should I not honor you? Should I not treat you with Ihsaan (kindness)? Should I not tell you those 10 things, which when you perform, Allah (Subhanahu Wa Ta’ala) will forgive all your sins, whether they are of the past or of the future, the new or the old, whether they were committed unwittingly or deliberately, whether they are small or big, whether they were done openly or in secret.
Offer 4 raka’at, then He (Sallallahu alaihi wa sallam) described the manner of offering Salaat Ut Tasbeeh.
(Sunan Ibn Majah, Pg: No. 99)