Webb drove Pons's second car alongside Meindert van Buuren at Monza and Aragon, and will also contest the forthcoming Monaco race, but will then focus on his Signatech Alpine European Le Mans Series programme, with 18-year-old Colombian Tunjo taking his place.
The team said Tunjo's deal covered the 2015 FR3.5 season too.
Pons team manager Emilio de Villota said: "We are extremely happy to have reached an agreement with Oscar Tunjo, one of the best young drivers emerged from the FRenault 2.0 arena.
"I've been chasing him for quite some time and I'm very satisfied to finally have him in our line-up.
"We'll be using the rest of the 2014 season in order to prepare for 2015, a year that we hope will see us among the frontrunners."
Tunjo graduates to FR3.5 after finishing sixth in last year's Formula Renault 2.0 Eurocup. He tested the FR3.5 car with the Charouz-run Lotus team at the end of 2013.
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