The 39-year-old completed his takeover, which could cost in excess of £100million if clauses are triggered, on Tuesday.
Relegated Villa won the European Cup in 1982 but dropped out of the Premier League last season, winning just three games.
They are preparing for their first season out of the top flight since 1987 but Chinese businessman Xia has targeted a return to their glory days.
“We don’t have a very detailed plan but we have a vision that we will challenge to get back into the Premier League and we will be challenging when we get back,” he said.
“The aim, not just the hope, is to get back in European field within five years and I wish we can succeed to get another trophy like we have here in eight or 10 years.
“That is not an exact number, but we want to win the European Cup.
“After we get back to the Premier League we have to know who are the other teams we need to compete with.
“You have to know the whole system of this business and you have to know who else you have to compete with.”
Villa are close to signing Bournemouth captain Tommy Elphick and are discussing personal terms for the 28-year-old who won the Championship with the Cherries in 2015.
The club are reviewing their recruitment and are considering appointing a technical director to aid new boss Roberto Di Matteo after the former regime blew around £55million on signings last summer.
Sporting director Hendrik Almstadt left in March and Xia was critical over the role current director of scouting and recruitment Paddy Riley has played.
“Honestly, everyone should agree with me, that he didn’t do too well,” he said.
“So people should understand what he has to do, what responsibility he has to take. We will discuss this very shortly.”