Emmanuel Adebayor to lead Real's front line
The Spanish club announced the deal Tuesday on its website, saying it has "a unilateral option" to purchase the 26-year-old in the offseason.
No financial details were released, but Spanish COPE Radio earlier said Madrid will pay €4 million ($5.5 million) for the Togolese forward, who had been little used at the Premier League club after falling down the pecking order.
That amount is what Adebayor was reportedly set to earn for the remainder of the current season.
Madrid can buy Adebayor at the end of the season with COPE putting the price tag at €17.4 million ($23.7 million).
Manchester City said Adebayor would undergo his medical in the Spanish capital on Wednesday.
Madrid coach Jose Mourinho is desperate to bolster his attack, with Gonzalo Higuain injured and Karim Benzema on unconvincing form.
Argentina striker Higuain is out until at least April after undergoing back surgery while Benzema hasn't failed to secure a regular starting spot. The France striker scored only his second league goal of the campaign in Sunday's 1-0 win over Mallorca.
Madrid can ill-afford to drop points as it chases Spanish leader Barcelona, which has won 14 straight league games to hold a four-point advantage over its biggest rival.
Mourinho had warned at the start of the season he couldn't afford to lose either of his two strikers due to limited backup options at the position.
Adebayor offers a physical presence inside the box similar to Didier Drogba, who was one of the catalysts for Mourinho's successful spell at Chelsea.
The 2008 African Footballer of the Year helped Monaco to the 2004 Champions League final where the French club lost to Mourinho's FC Porto.
He joined Arsenal in January 2006 where he scored 62 domestic goals in three years before heading to City, where his playing time has dropped off dramatically under Roberto Mancini.
City's plethora of international attackers - Carlos Tevez, Mario Balotelli and recent signing Edin Dzeko - were favored over Adebayor in Mancini's attack.
Adebayor, a former Togo international, scored 19 goals in 36 appearances for City.