Sheikh Sulaymân al-Tuwayjirî
Allah says: "Pilgrimage to the house is a duty that humanity owes to Allah, those who have the means to undertake the journey." [Sûrah Al `Imran: 97]
The performance of Hajj is not obligatory upon a poor person who cannot afford to undertake it.
Zakâh is paid to those who are entitled to recieve it. Therefore, if a person is genuinely poor and is eligible to receive Zakâh on account of his poverty, then he may do as he pleases with any Zakâh funds that he receives. If he wishes to use those funds to perform Hajj, he is free to do so and his Hajj will be valid.
It is not necessary to pay a person Zakâh so that he will be able to perform Hajj, since Hajj is not obligatory for a person who cannot afford it. However, if a person pays his Zakâh to a recipient who is genuinely poor and then the recipient decides to perform Hajj with it, there will be no liability for this upon the person who paid him the Zakâh.
Source: Islam Today