Slim already made a similar deal at Spanish real estate company Realia, a unit of FCC on which he launched a full takeover bid on Jan. 28.
Jarque, whose appointment is effective from Tuesday, replaces Juan Bejar, who signalled he would resign as CEO after Carlos Slim bought the FCC stake.
Slim wants to replace Chief Executive Juan Bejar with Carlos Jarque, 60, the head of international, corporate and governmental affairs at América Móvil.
The companies will work together on projects in the Americas excluding Mexico.