Areola agreed a five-year contract with the Hammers and will compete with Lukasz Fabianski for the role of first choice keeper at the London Stadium.
The 29-year-old said: “I feel great. I’m happy to sign and happy to stay here permanently and I can’t wait to start to train and to do the job.
“The main thing is that I felt the love of the supporters last season. Something for me that is really important is to feel that I’m loved.
“I know that I have to do my job and to do everything to make them happy, and obviously also the team. The vibe of last season was great, so I just wanted to do everything to stay here.”
West Ham boss David Moyes was pleased to get Areola back to the club.
“Alphonse made a huge contribution to the club during his loan spell last season. His performances backed up why we see him as a top goalkeeper,” he said.
“He brings proven quality and experience at the highest level, both on the domestic and international scene.”