Taken from Gitagovindam of Jayadeva
Dasavatara Stotram-The Prophecy About Appearians of Kalki in kali Yuga
प्रलयपयोधि जले धृतवानसि वेदं – विहित वहित्रचरित्रमखेदम् । केशव धृत मीनशरीर – जय जगदीश हरे ॥ १.५ ॥
क्षितिरतिविपुलतरे तव तिष्ठति पृष्ठे
धरणीधरणकिनचक्रगरिष्ठे ।
केशव धृत कच्चपरूप- जय जगदीश हरे ॥ १.६ ॥
वसति दशनशिखरे धरणी तव लग्ना
शशिनि कलङ्क कलेव निमग्ना ।
केशव धृत सूकररूप-जय जगदीश हरे ॥ १.७ ॥
तव करकमल वरे नखमद्भुत शृङ्गं
दलित हिरण्य कशिपु तनुभृङ्गम् ।
केशव धृत नरहरि रूप-जय जगदीश हरे ॥ १.८ ॥
छलयसि विक्रमणे बलिमद्भुत वामन
पदनखनीरज नितजन पावन ।
केशव धृतवामनरुप-जय जगदीश हरे ॥ १.९ ॥
क्षत्रीयरुधिरमये जगदपगतपापं
स्नपयसि पयसि शमितभवतापम् ।
केशव धृतभृगुपतिरूप-जय जगदीश हरे ॥ १.१० ॥
वितरसि दिक्षु रणे दिक्पति कमनीयं
दशमुखमौलिबलि रमणीयम् ।
केशव धृत रामशरीर-जय जगदीश हरे ॥ १.११ ॥
वहसि वपुषि विषदे वसनं जलदाभं
हलहतिभीतिमिलितयमुनाभम् ।
केशव धृत हलधर रूप-जय जगदीश हरे ॥ १.१२ ॥
निन्दसि यज्ञ विधेरहह श्रुतिजातम्
सदयहृदय दर्शित पशुघातम् ।
केशव धृत बुद्धशरीर-जय जगदीश हरे ॥ १.१३ ॥
म्लेच्छ निवहनिधने कलयसि करवालं
धूमकेतुमिव किमपि करालम् ।
केशव धृतकल्किशरीर-जय जगदीश हरे ॥ १.१४ ॥
(1) O Kesava! O Lord of the universe! O Lord Hari! You assume the form of a giant fish to protect the Vedas, from the turbulent sea of devastation.
(2) O Kesava! O Lord of the universe! O Lord Hari, you have assumed the form of a tortoise! In this incarnation as a divine tortoise the great Mandara Mountain rests upon Your gigantic back as a pivot for churning the ocean of milk. From holding up the huge mountain a large scar-like depression is put in Your back, which has become most glorious.
(3) O Kesava! O Lord of the universe! O Lord Hari, you have assumed the form of a boar! The earth, which had become I, merged in the Garbhodaka Ocean at the bottom of the universe, sits fixed upon the tip of Your tusk like a spot upon the moon.
(4) O Kesava! O Lord of the universe! O Lord Hari, you have assumed the form of half-man, half-lion l lust as one can easily crush a wasp between one’s fingernails, so in the same way the body of the wasp like demon Hiranyakasipu has been ripped apart by the wonderful pointed nails on Your beautiful lotus hands.
(5) O Kesava! O Lord of the universe! O Lord Hari, you have assumed the form of a dwarf-brahmana! O wonderful dwarf, by Your massive steps You deceive King Bali, and by the Ganges water that has emanated from the nails of your lotus feet, You deliver all living beings within this world.
(6) O Kesava! O Lord of the universe! O Lord Hari, you have assumed the form of Bhrgupati [Parasurama] ! At Kuruksetra You bathed the earth with the blood from the bodies of the demoniac rulers killed by you. The sins of the world are washed away by You, and because of You people are relieved room the blazing fire of material existence.
(7) O Kesava! O Lord of the universe! O Lord Hari, you have assumed the form of Ramacandra! In the battle of Lanka You destroy the ten-headed demon Ravana and distribute his heads as a delightful offering to the presiding deities of the ten directions, headed by Indira. This action was long desired by all of them, who were much harassed by this monster.
(8) O Kesava! O Lord of the universe! O Lord Hari, you have assumed the form of Balarama, the yielder of the prowl On Your brilliant white body You wear garments the color of a fresh blue rain cloud. These garments are colored like the beautiful dark hue of the River Yamuna, who feels great fear due to the striking of Your plowshare.
(9) O Kesava! O Lord of the universe! O Lord Hari, you have assumed the form of Buddha (Adi Buddha and not Goutam Sakya Muni)! With a compassionate heart, you decried the slaughtering of helpless animals sacrificed in the name of Yagna rituals.
(10) 0 Kesava! O Lord of the universe! O Lord Hari, you would assume the form of Kalki! You would appear like a comet and carry a terrifying sword for bringing about the annihilation of the wicked mleccha barbarians ain the Kali-yuga.
NOTE: The prophecy is also available in Bhagavad Purana (Canto 12 Chapter 2:12-16), again it is mentioned in Vishnu, Matsya, and Garuda Purana. Kalki Puran is a fraudulent and unreliable source, thus not mentioned.
Paritranaya sadhunam
vinasaya ca duskrtam
dharma-samsthapanarthaya
sambhavami yuge yuge.
To protect the pious and preserve the Dharma I, the God shall appear again and again..
The above sloka of the Bhagavat Gita is the indication of Kalki’s appearance.