The Monaco star has been a doubt for the tournament since suffering cruciate knee ligament damage during a Coupe de France tie in January.
However, the former Atletico Madrid man said last month he was "satisfied" with his recovery and Pekerman has opted to name the talismanic striker in his initial 29-man squad.
Falcao scored nine goals in 13 appearances during qualifying and forms part of an impressive line-up that also includes Jackson Martinez and Borussia Dortmund-bound Adrian Ramos.
There is also a place for highly-rated River Plate defender Eder Alvarez Balanta, with Fiorentina winger Juan Cuadrado, Inter's Fredy Guarin and James Rodriguez among the options in midfield.
Colombia begin their World Cup campaign against Greece in Group C on June 14.
Squad in full:
Defenders: Santiago Arias (PSV), Pablo Armero (Napoli), Eder Alvarez Balanta (River Plate), Aquivaldo Mosquera (America), Luis Perea (Cruz Azul), Carlos Valdes (San Lorenzo), Mario Yepes (Atalanta), Cristian Zapata (Milan), Camilo Zuniga (Napoli)
Midfielders: Abel Aguilar (Toulouse), Juan Cuadrado (Fiorentina), Fredy Guarin (Inter), Victor Ibarbo (Cagliari), Alex Mejia (Atletico Nacional), Juan Fernando Quintero (Porto), Aldo Ramirez (Morelia), James Rodriguez (Monaco), Carlos Sanchez Moreno (Elche), Elkin Soto (Mainz), Macnelly Torres (Al Shabab), Edwin Valencia (Fluminense)
