The La Liga giants will then have an option to sign the 26-year-old on a permanent basis.
Adebayor, who had been pushed to the fringes of the City squad, has already scored twice for his new club, netting in wins over Sevilla and Real Sociedad.
"I'm very happy for scoring two goals," Adebayor told a press conference in Madrid.
"I will work hard every day to help win our games.
"It is very easy to work with Mourinho. He is an excellent person and he enhances my game.
"He has his own way of dealing with people. He tells you what he expects you to do."
The change of scenery looks to have sparked an upturn in the Togolese striker's fortunes, and the presence of several English-speaking team-mates has allowed him to settle.
"I want to thank my team-mates for helping me adapt so easily to this league championship.
"Granero, Ramos, Ronaldo, Pepe, Marcelo. They all speak English, so they understand me and I understand them. I am very happy to be here."
Real Madrid are seven points behind leaders Barcelona in the Spanish top flight, but Adebayor vowed: "We will fight to the end to win every title."
The 26-year-old also gave an insight into the lasting impression the deadly terrorist attack on Togo's team bus ahead of last year's African Nations Cup has had on him.
"Luckily, I still have both my legs and can play football," he said.
"I sometimes mistake loud noises for bullets, but I'm over it now and ready to work."