Allah the Exalted said: "Indeed, Allah sends His blessings upon the Prophet, and so do His angels. O you who believe, invoke blessings upon him and salute him with a worthy salutation." (33:56).
The Messenger of Allah ﷺ said: "Whoever invokes one blessing upon me, Allah will send ten blessings upon him in return." [Muslim 384].
The Messenger of Allah ﷺ said: "Do not make my grave a place of festival,¹ but invoke blessings upon me, for your salutations reach me wherever you may be." [Abu Dawud 2042; Ahmad 2/367; Sahih al-Jami‘ as-saghir 7226].
The Messenger of Allah ﷺ said: "The miserly one is he in whose presence I am mentioned and who does not invoke blessings upon me." [at-Tirmidhi 3546; Ahmad 1/201; Sahih al-Jami‘ as-saghir 2878; Sahih Sunan at-Tirmidhi 3/177].
The Messenger of Allah ﷺ said: "Indeed, Allah has angels who travel the earth and convey to me the salutations of my community." [an-Nasa’i 1282; al-Hakim 2/421; Sahih al-Jami‘ as-saghir 2174].
The Messenger of Allah ﷺ said: "No one greets me except that Allah returns my soul to me² so that I may return his greeting." [Abu Dawud 2041; Ahmad 2/527; Sahih Sunan Abu Dawud 1/383].
¹That is, a place to which people flock for festivities — as they once did for idols. The Prophet's ﷺ grave should be visited only to greet him and to supplicate [Ibn Taymiyyah, Iqtida’].
²The meaning is that Allah, by His power, arranges for the Prophet ﷺ to respond to every greeting addressed to him; the details of this are known to Allah alone [see an-Nawawi, Sharh Muslim; Ibn al-Qayyim, Jala’ al-afham].