The newly-promoted side have signed the Colombia international on a one-year contract.
Falcao arrives on a free transfer after terminating his contract with Turkish outfit Galatasaray on Wednesday.
The 35-year-old joined Galatasaray from AS Monaco in the summer of 2019 and scored 20 goals in 43 games.
Falcao will be making a return to the Spanish La Liga eight years after last turning out for Atletico Madrid, where he scored 70 goals in 91 appearances and won the Europa League, Copa del Rey and UEFA Super Cup.
The former FC Porto striker captained Monaco to the Ligue 1 title in the 2016/2017 season but also had a forgettable loan spells at Manchester United and Chelsea while on the books of the French club.
Falcao is Colombia’s all-time top scorer with 35 goals in 91 games.
Rayo Vallecano are currently 10th on the La Liga table, boasting two defeats and a win in their opening three games.
The Franjirrojos will travel to Levante in their next game after the international break when Falcao could make his debut for the club.
