The Colombia international has joined the Premier League champions on a temporary deal from Ligue 1 side Monaco until the end of the 2014/15 campaign.
Falcao endured a miserable season-long loan spell at Manchester United last term but it didn’t put Mourinho off snapping up the South American.
And the 53-year-old manager revealed Cahill and Terry endorsed the west London side’s move for the former Atletico Madrid striker.
“I watched our game against Manchester United a few times,” Mourinho is quoted as saying by Daily Mail.
“I spoke with John and Cahill a lot about him and we think the bright movement is there, the movement to get freedom in the box to score goals is there.
“Our players had difficulty to control him and we feel the potential is there. Let’s see if he can improve his confidence, his happiness.”
Falcao will linked up with his former Atletico Madrid team-mates Thibaut Courtois and Filipe Luis at Stamford Bridge.
The South American memorably scored a hat-trick against Chelsea in a 4-1 victory over the then-Champions League holders in the Uefa Super Cup in Monaco.
Falcao scored 52 times in 68 La Liga games before his move to Monaco in 2013.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news