The Portuguese attacker signed his new deal at Valley Parade this (Thursday) morning after his original short-term contract had expired on Sunday.
Morais started four of City's first seven games at the beginning of the campaign after first signing on with the Bantams on the eve of the club's season opener with Coventry City.
Speaking about Morais' new deal, Bantams boss Phil Parkinson said: "Filipe has decided to stay with us until January.
"I like him as a player and as a person and I think he has made a good contribution to the season so far. I was particularly impressed with his performance away at Crawley - I thought he was excellent.
"He had offers to go elsewhere on longer contracts but he was keen to stay here and keep proving himself at Bradford.
"He has played a lot of games at this level and he gives us another attacking option. He can play as an out-and-out wide player, he can play in behind the strikers or he can play as one of our three central midfielders if we stick with that.
"He has plenty of flexibility to his game and he is a good signing for us."