Hadith: When Allah created Adam (peace be upon him), He said to him: Go and greet those – a group of angels who were sitting – and listen to what they are going to say in response to your greeting as that will be your greeting and the greeting of your offspring

عن أبي هريرة رضي الله عنه عن النبي صلى الله عليه وسلم قال: «لما خلق الله آدم صلى الله عليه وسلم قال: اذهب فَسَلِّمْ على أولئك -نَفَرٍ من الملائكة جلوس- فاستمع ما يُحَيُّونَكَ؛ فإنها تَحِيَّتُكَ وتحية ذُرِّيتِكَ. فقال: السلام عليكم، فقالوا: السلام عليك ورحمة الله، فَزَادُوهُ: ورحمة الله».
[صحيح] - [متفق عليه]

Abu Hurayrah (may Allah be pleased with him) reported that the Prophet (may Allah's peace and blessings be upon him) said: "When Allah created Adam (peace be upon him), He said to him: 'Go and greet those – a group of angels who were sitting – and listen to what they are going to say in response to your greeting as that will be your greeting and the greeting of your offspring.' He (Adam) said: 'As-Salāmu ‘alaykum (peace be upon you).' They replied: 'As-Salāmu ‘alayk wa rahmatullāh (Peace and mercy of Allah be upon you),' thus adding 'wa-rahmatullāh (and mercy of Allah)' in their response to his greeting."
[Authentic hadith] - [Narrated by Bukhari & Muslim]

Explanation

When Allah created Adam, He ordered him to go to a group of angels and greet them with peace and then listen to their response to his greeting because that would be the prescribed greeting for him and his offspring after him who follow the religion of the messengers. So he said: As-Salāmu ‘alaykum (peace be upon you), and they replied: As-Salāmu ‘alayk wa rahmatullāh (peace and mercy of Allah be upon you), adding 'rahmatullāh' (mercy of Allah). This has, thus, become the prescribed wording when greeting and returning the greeting. Other Hadīths had the addition: "wa rahmatullāh wa barakātuh (...and mercy of Allah and His blessings be upon you!)"