The England international wore the new shirt for the first time on Sunday evening on his return to club action, as the Red Devils slumped to a 1-0 loss to Bayern Munich.
United confirmed after the friendly in Bavaria that Rashford will carry the number permanently, taking over from Zlatan Ibrahimovic who left the club during the 2017-18 campaign.
Mourinho feels that the academy product deserves the shirt after waiting patiently for his chance, telling MUTV: "He wanted it. He always wanted it.
"Of course, he respected the big [Wayne] Rooney and then Zlatan wanted to have it. Of course, he was in the shadow, waiting for the opportunity and now the shirt is empty. It's something fantastic for the kid, let's give the shirt to him."
Rashford, previously number 19 at United, failed to make an impact during his 65 minutes on the field against Bayern.