A large number of Muslims belive it is permissable and highly recommend to visit the prophets grave after they do Hajj. This belief is based on a hadeeth which they think is authentic. However this hadeeth is extremely weak and should not be acted upon.
The narration in question says the prophet Mohammed said “Whoever made hajj and visited me after my death (it) is like (he) visited me during my life” Imam Tabarani narrated it in his “Mojam al-Kabeer”
Imam Ahmad said: Matrook (rejected) al-hadeeth in Mizanul itidal (1/558/#2121). Ibn Hajar in “Taqreeb” said, Matrook (rejected) al-hadeeth. Nasai in “Duafa” (#134) said, Matrook (rejected) al-hadeeth. Sheikh Albani in “Daeef al jamee” said the narration is fabricated.
The reason this hadeeth is very weak is because of the a narrator in the chain of narration who went by the name of Khafs ibn Abe Dawud however his real name was Khafs ibn Sulayman and Ibn Khirash said on him: Kadhab (liar)! Fabricated narrations (he makes up hadeeth).
Also this hadeeth goes against an authentic hadeeth which indicates a person should only make religious journeys to three places and the prophets grave is not one of the places mentioned.
The Prophet said: “No (religious) journey should be undertaken to visit any mosque but three: al-Masjid al-Haraam (in Makkah), the Mosque of the Messenger (in Medina) and the Mosque of al-Aqsa (in Jerusalem)” Recorded by Bukhari and Muslim.
So the most correct thing to intended and act upon is to visit the prophets mosque in Medina when your Hajj is finished. While visiting his mosque you will be able to see his grave as well, but your intention can not be to travel from Makkah to Medina just to visit his grave, as this religious journey is not allowed because it goes against what the prophet has ordered us to do in the hadeeth just mentioned.