The Spanish giants also have the option of signing the Togolese international permanently at the end of the season.
Real Madrid sign Adebayor on loan from Man City
The 26-year-old Togolese international travels to Madrid today to undergo a medical.
Real will have the option to sign Adebayor on a permanent basis at the end of the season and Spanish media reports said they could pay around €15 million (Dh75.43m) for him.
A statement on the Real Madrid website said: “Real Madrid CF and Manchester City FC have reached a deal that will see Emmanuel Adebayor play on loan for the former club.
“The player will remain at Real Madrid until the end of the current season, at which point the club hold a unilateral option to purchase the player.”
The powerful frontman will provide Jose Mourinho, the Real coach, with an extra attacking option following a back injury t0 the Argentine striker Gonzalo Higuain that will sideline him until around April.
Mourinho has been pushing the club for another centre-forward since arriving from Inter Milan last year and with Higuain's injury and Karim Benzema's failure to live up to expectations the pressure had grown during January.
France striker Benzema has only scored two league goals this season as Real chase La Liga leaders Barcelona, prepare for a Copa del Rey semi-final and the Champions League knockout stages.
Real's first choice as a stand-in appeared to be their former striker Ruud van Nistelrooy but SV Hamburg refused to release him.
Moving for Adebayor, the 2008 African Player of the Year, had the added bonus that he is a free to play for Real in the Champions League.
Adebayor started his career in France with Metz and AS Monaco before making his name after signing for Arsenal in 2006.
He scored 62 goals in 142 appearances in all competitions with Arsene Wenger's side before moving to Manchester City on a five-year contract in 2009 for around £25m.
He managed 19 goals in 36 starts for City but has dropped out of the reckoning this season and was pushed further towards the door when City signed the Bosnian striker Edin Dzeko this month.