The 24-year-old defender moved from Ajax on Monday after coming through the Dutch club's youth setup.
While Alderweireld was linked with a host of other clubs over the close-season, he claims on-loan Chelsea goalkeeper Courtois sold the club to him.
"I said Atletico were interested in me and he (Courtois) told me how great it is, this team and its fans," the defender told Atletico's official website.
"He advised me to come because he is very happy here."
Diego Simeone also swooped for French midfielder Josuha Guilavogui on the final day of the transfer window, bringing the 22-year-old in from Saint-Etienne.
The France international believes his new side can challenge for honours in years to come, after Atletico clinched the Copa del Rey title last season.
"I am pleased to reach such a big club like Atletico and play with fantastic fans," he said.
"I hope to work hard for the team to continue winning titles in the coming years."
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