The 23-year-old Ghana international has signed a five-year contract at Villa Park.
"I am really pleased to bring Jordan to the football club," manager Tim Sherwood told the Villa website.
"He is a fantastic young player who is perfectly suited to the Premier League."
Villa have also agreed a deal to sign Cordoba fullback Jose Angel Crespo, the Spanish club said.
The 28-year-old has been in a contractual dispute with the Andalusian side following their relegation from La Liga last season and has been looking for a move away.
"Cordoba and Aston Villa have reached an agreement for the transfer of Jose Angel Crespo to the English club," Cordoba said on Twitter.
"The defender...will travel to England today for a medical ahead of the signing."
Villa, who sold striker Christian Benteke to Liverpool this month, have also signed French defender Jordan Amavi and Senegal midfielder Idrissa Gueye from Ligue 1 clubs since the end of last season.
(Reporting by Tim Hanlon; Editing by Ed Osmond)
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