The Republic of Ireland Under-21 international was allowed to remain with Shamrock for the first half of the campaign and compete in the Europa League before moving to Villa in January.
And boss Alex McLeish is hoping Stevens can quickly adjust to the demands of the Premier League and provide competition for Stephen Warnock.
He said: "It will be nice to have another body in the squad and Enda is a player who has got some potential.
"He's a young player, there was a wee bit of interest in him and we decided to sign him.
"It is up to Enda to hit the ground running and do well and leave me thinking: 'let's get this guy involved.'
"Enda will have to go some way to break in because Stephen Warnock has been in great form.
"But we are hoping when he joins, he will get to grips with everything, adapt very quickly to put pressure on guys like Stephen."
Stevens, who signed a pre-contract agreement, will officially become a Villa player when the transfer window reopens on Monday.
The Dublin born player had spells with UCD and St Patrick's Athletic before joining Shamrock in December 2009 and helping them to win the league title at the end of his first season.
Stevens made his Under-21 debut against Cyprus 10 months ago.