Given has signed a five-year deal after moving to Villa Park from Manchester City, despite being 35 years of age. But he insisted the length of the contract does not faze him, with both the Republic of Ireland international and boss McLeish pointing to Given's predecessor in the Villa goal, Brad Friedel, as an example.
"I'm not frightened by the five years, I'm quite looking forward to a great spell at Aston Villa," he said.
"You look at Brad Friedel, who's 40 and just signed a two-year contract at Tottenham, and Edwin van der Sar, who was 40 last season and probably had one of the best seasons of his career, so in terms of age, I want to play football as long as I can."
McLeish said he picked Given out of an impressive shortlist of goalkeepers due to his international and Premier League record.
"There were some great goalkeepers out there, including Ben Foster, but Shay was a long-term target," he said.
"I admired his huge international experience, and having done diligence on him over the years, I know what kind of character he is.
"He's a good five years younger than Brad Friedel, and Brad is still getting contracts in the Premier League at a fantastic level.
"I felt that he had the gravitas to come and play here."
Source: PA
Source: PA