Rowe, 21, was released by the Premier League club last month having come up through Villa's youth academy.
His only first-team game came when he was part of a youthful Villa side that lost 4-1 to Liverpool in the FA Cup third round after an outbreak of Covid-19 sidelined the senior squad.
Former Crewe player Ray, 27, has agreed a two-year deal with the Grecians.
Rowe has also played three times for Villa's under-21 side in the EFL Trophy and had a spell on loan at Hereford as they made the FA Trophy final last season.
"Callum came to train with us for a couple of reserve matches at the end of last season. He has a fantastic physical profile and he really impressed us," said Exeter manager Matt Taylor.
"Character and personality is a huge attribute at this football club and he certainly fits the bill."
Exeter have not disclosed the length of Rowe's deal at St James Park.
Ray scored once in 23 appearances for Tranmere, coincidentally against an Aston Villa under-21 side featuring Rowe.
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