This is Chapter 4 of the famous work, known as The Burdah, sung by Manaqib Nasheeds.

Al-Busiri narrated the circumstances of his inspiration to write the Burdah:

...I had composed a number of praise poems for the Prophet, Allah bless Him and salute Him with peace, including one that was suggested to me by my friend Zayn al-Dīn Yʿaqūb b. al-Zubayr. Some time after that, I was stricken by fālij (stroke), an illness that paralyzed half of my body. I thought that I would compose this poem, and so I made supplications to the Prophet Muhammad, Allah bless Him and salute Him with peace, to intercede for me and (and ask God to) cure me. I repeatedly sang the poem, wept, prayed, and asked for intercession. Then I slept and in my dream, I saw the Prophet, Allah bless Him and salute Him with peace. He wiped my face with His blessed hands and covered me in His Mantle (Burdah). Then I woke up and found I was able to walk; so I got up and left my house. I had told no one about what had happened.

I encountered a Sufi (faqīr) on my way and he said to me: “I want you to give me the poem in which you praise the Prophet, Allah bless Him and salute Him with peace.”

I said: “Which one?”

So he said: ”The one that you composed during your sickness.”

Then he recited the first verse and said: “I swear by God that I heard it in a dream last night being sung in the presence of the Prophet Muhammad, Allah bless Him and salute Him with peace. I saw the Prophet, Allah bless Him and salute Him with peace, was pleased with it and covered the person who sang it with His Mantle.”
So I recited the poem to him and he memorized it and related his vision to others. 
— Imam al-Busiri

The Burda is divided into 10 chapters and 160 verses all rhyming with each other. Interspersing the verses is the refrain, "My Patron Deity, confer blessings and peace continuously and eternally on Your Beloved, the Best of All Creation" (Arabic: مولاي صلي و سلم دائما أبدا على حبيبك خير الخلق كلهم). Each verse ends with the Arabic letter mīm, a style called mīmīya. The 10 chapters of the Burda comprise:
On Lyrical Love Yearning
On Warnings about the Caprices of the Self
On the Praise of the Prophet
On His Birth
On His Miracles
On the Exalted Stature and Miraculous Merits of the Qur'an
On the Ascension of the Prophet
On the Struggle of Allah’s Messenger
On Seeking Intercession through the Prophet
On Intimate Discourse and the Petition of One’s State.

Burdah Chapter 4 (Manaqib Nasheeds) 01 - 05 - 16

Manaqib Nashids