The panda will join a female called Ember while the spider monkey will join a troop consisting of females Luna and Lena and male Kikou.
Zookeepers said the monkey would initially remain off-show to visitors while the primates were introduced.
Mammal keeper at Paignton Zoo James Shora said: “The red pandas offer those quieter, more contemplative moments, while the spider monkeys bring incredible dynamic energy from the forest canopies of South America.
“It’s like having two completely different worlds side by side.”
The red panda came from Les Terres de Natae, Pont-Scorff and the brown spider monkey from Zoo Amiens Métropole.