If he does the farewell tawaaf, he should go out walking normally and should not walk with his face towards the Ka’bah
Question

                Some of the pilgrims, after performing the farewell tawaaf, do not turn their backs towards the Ka’bah, rather they walk backwards, with their faces towards the Ka’bah, until they exit the Mosque. Is this part of the Sunnah?.
Praise be to Allah.This action is not part of the Sunnah, rather 
    it is a reprehensible innovation. This is what some people do, claiming to venerate the Ka’bah thereby. If this was really a sign of respect for 
    the Ka’bah, you would find that the Prophet  (peace and blessings of Allaah be upon him) and the Sahaabah did that, but there are no reports 
    to suggest that. 
Shaykh Ibn Baaz said: 
When (the pilgrim) has finished bidding 
    farewell to the House and wants to leave the mosque, he should walk normally, facing forwards, until he exits. He should not walk backwards, 
    because there is no report that the Prophet  (peace and blessings of Allaah be upon him) or his companions did this, rather it is an 
    innovation (bid’ah). The Prophet  (peace and blessings of Allaah be upon him) said, “Whoever does any action that is not part of this matter 
    of ours (i.e., Islam) will have it rejected.” Narrated by Muslim, 1718. And he  (peace and blessings of Allaah be upon him) said: “Beware of 
    newly-invented matters, for every newly-invented matter is an innovation and every innovation is a going astray.” Narrated by Abu Dawood, 4607; 
    classed as saheeh by al-Albaani in Saheeh Abi Dawood. We ask Allaah to make us steadfast in adhering to His religion, and to keep us safe 
    from anything that goes against it, for He is the Most Generous, Most Kind. 
Shaykh Ibn ‘Uthaymeen said, when listing the 
    mistakes that some people make during the farewell tawaaf: 
Some of them exit the mosque, after the farewell tawaaf, walking backwards, claiming that they 
    are venerating the Ka’bah thereby. This goes against the Sunnah, rather it is the kind of innovation (bid’ah) against which the Messenger of 
    Allaah  (peace and blessings of Allaah be upon him) warned us when he said: “Every innovation is a going astray.” Innovation (bid’ah) means 
    everything that has been invented in ‘aqeedah (belief) or ‘ibaadah (worship) that goes against the way of the Messenger of Allaah  (peace and 
    blessings of Allaah be upon him) and his Rightly-Guided Caliphs. Does this person who walks backwards and claims to be venerating the Ka’bah think 
    that he is venerating it more than the Messenger of Allaah  (peace and blessings of Allaah be upon him) did? Or does he think that the Prophet 
     (peace and blessings of Allaah be upon him) and the Rightly-Guided Caliphs did not know that this was an act of veneration towards the 
    Ka’bah?! 
Manaasik al-Hajj wa’l-‘Umrah, 
    p. 135. 
Fataawa al-Shaykh Ibn Baaz, 
    16/98.