The Manchester City striker is in the Spanish capital to complete a move for the rest of the season.
After undertaking tests on the Togo striker, Real Madrid's chief of medical services Carlos Diez told the club's website: "He is a physical marvel. He is in very good physical condition and will be able to immediately be incorporated into the team."
Madrid will sign Adebayor on loan with an option to buy the 26-year-old in the summer.
Adebayor is needed at the Bernabeu as Gonzalo Higuain is injured, leaving only the inconsistent Karim Benzema to lead the attack.
He was initially a massive hit at City following his £25million move north from Arsenal 18 months ago, scoring in his first four games, but his star faded after Roberto Mancini replaced Mark Hughes as manager.