Club Atlético de Madrid have signed Falcao and Rúben Micael from FC Porto for a combined fee that could rise to €52m.
Falcao, who struck a record-breaking 17 goals in the Dragons' triumphant UEFA Europa League run last season, has cost the 2010 winners a reported €40m, with a further €7m due in possible add-ons. It was only last month that the striker extended his contract with Porto to 2015.
"I am very happy to be here; I hope to give the club a lot of happiness," said the Colombian international. "I have come to a very big team with fantastic supporters and to play in the biggest league in the world. There is a hunger here within this team to achieve important goals. [Being the club's record signing] is a big responsibility and I want to give my all in order to repay that out on the pitch."
The 25-year-old has signed a five-year deal at the Vicente Calderón and will fill the void created by the departure of Sergio Agüero to Manchester City FC. Overall, Falcao registered an impressive 41 goals in 51 Liga appearances for Porto following his transfer from CA River Plate in 2009.
Rúben Micael, also 25, has penned the same length of contract as Falcao after completing a transfer reportedly worth €5m, but will spend the forthcoming campaign on loan at Real Zaragoza. The Portugal midfielder, who scored twice on his international debut against Finland earlier this year, joined Porto from CD Nacional in January 2010.
The Rojiblancos are in the driving seat to reach the UEFA Europa League group stage after a 2-0 home success against Vitória SC in the first instalment of their play-off tie. Porto face FC Barcelona in the UEFA Super Cup on 26 August.