Among other things, they are capable of thinking logically, of recognising themselves in the mirror and of empathy, the study said.
"The mental abilities of corvids and parrots are as sophisticated and diverse as those of apes," said one of the researchers Onur Gunturkun from Ruhr University Bochum in Germany.
The findings were published in the journal Trends in Cognitive Sciences.
In mammals, cognitive skills are controlled by the multi-layered cerebral cortex, also called neocortex.
This brain structure does not exist in birds. Instead, complex mental tasks are managed by the so-called pallium.
Moreover, birds have much smaller brains than apes. While ape brains weigh 275 to 500 gram on average, birds, who are just as skilful despite lacking a cortex, only manage five to 20 gram.
"How, then, are birds capable of the same cognitive performance as apes?" Gunturkun asked.
To address this question, the researchers compiled studies which had revealed diverse cognitive skills in birds and analysed numerous neuro-anatomic studies.
They found that brains of birds and mammals have some similarities.
Single modules of the brains, for example, are wired in a similar way, and both animal groups have a prefrontal brain structure that controls similar executive functions.
It is not known how these similarities have evolved.
The researchers believe that either their last common ancestor passed the neuronal basis to birds and mammals or - and the authors consider this more likely - they evolved independently of each other, because both animal groups faced the same challenges.
According to the researchers, this would mean that certain wiring patterns in the brain are necessary to boost cognitive performance.
"What is clear is that the multi-layered mammalian cortex is not required for complex cognition," Gunturkun noted.
"The absolute brain weight is not relevant for mental abilities, either," Gunturkun said.