The Shani stotra was composed by King Dashratha, the father of Lord Rama, to please and gain the blessings of Shani Dev. Shani enters the star constellation of Rohini once in every 30 years. The scriptures say “Kings will die and kingdoms will fall when Shani enters Rohini”. It is said that during the reign of King Dasaratha when Shani was about to enter Rohini Nakshatra, King Dasaratha worshiped Shani and pleased with his prayers, Shani did not enter Rohini during the reign of King Dasharatha. Hence the Dasaratha Shani stotras are considered an excellent remedy for Saturn related troubles.

There are many famous versions of Shani Stotram, mentioned in Padma Puran, Skandh Puran, and Bramhand Puran.
This recitation is taken from Bramhand Puran.