The Stotra is Indra Krita Lakshmi Stotram, from the Devi Bhagavata Purana, 9th Canto, Chapter 42, and was chanted by Lord Indra to Goddess Mahalakshmi.
The original Devi Bhagavata chapter seems to have lots of additional prayers made by Indra to Goddess Mahalakshmi along with the offering of the sixteen Upacharas, before the commencement of the actual stotra.
The complete Sanskrit text of Devi Bhagavata 9.42 (containing the Dhyana Shloka, Shodasha Upachara Puja and Mahalakshmi Stotra) can be found on pages 683-686 of this pdf of the Sanskrit version of the Purana.
The Sanskrit text of only the stotra can be found on this page.
As found on the sanskritdocuments website, the actual Stotra seems to be Devi Bhagavata 9.42.8-10.5 and 9.42.51-75.
This stotra comes in connection with the legend of Samudra Mathana. According to the story, when Sage Durvasa gifted a garland (given to him by Lord Vishnu and Devi Mahalakshmi) to Lord Indra, Indra disrespected the gift, and thereby was cursed by Durvasa to lose all prosperity and Grace of Mahalakshmi. In order to regain their prosperity, the Devas along with the asuras churned the ocean of milk and obtained, among other treasures, Amrita and Goddess Mahalakshmi's blessings.
After the churning completed successfully, Indra worshipped Lord Vishnu, and then offered his prayers to Mahalakshmi through this Stotra.
For the benefit of the reader, I'm quoting the first shloka from the question, along with the translation by Swami Vijnanananda.
sahasradalapadmasthakarNikAvAsinIM parAm |
sharatpArvaNakoTInduprabhAmuShTikarAM parAm || 1||
svatejasA prajvalantIM sukhadRRishyAM manoharAm |
prataptakA~nchananibhashobhAM mUrtimatIM satIm || 2||
ratnabhUShaNabhUShADhyAM shobhitAM pItavAsasA |
IShaddhAsyaprasannAsyAM shashvatsusthirayauvanAm |
sarvasampatpradAtrIM cha mahAlakShmIM bhaje shubhAm || 3||
“O Mother! Thou residest on the thousand-petalled lotus. The beauty of Thy face excels the beauty of koti autumnal Full Moons. Thou art shining with Thy own splendour. Thou art very beautiful and lovely; Thy colour is like the burnished gold; Thou art with form, chaste, ornamented all over with jewel ornaments; Thou art wearing the yellow cloth and look! What beauty is coming out of it! Always a sweet smile reigns on Thy lips. Thy beauty is constant; Thou art the bestower of prosperity to all. O Mahâ Laksmî! I meditate on Thee.”