The Brazil under-23 captain announced his arrival at Villa Park in spectacular fashion with a superb goal against Bournemouth last weekend.
Luiz was making his full debut for Villa having joined in a £15million move from Manchester City, his summer capture is regarded as nothing less than a significant coup by the Villa’s hierarchy.
The 21-year-old remains highly-rated by the Premier League champions and their boss Guardiola.
But City's failure to secure a work permit for Luiz since signing him from Vasco De Gama in 2017 meant they were left with little option but to move him on, with Villa taking advantage of the situation to secure a player Smith expects to play a major role in his team.
The Villa boss said: “Douglas is Pep’s loss and my gain. I met Pep recently at the League Managers’ meeting and he spoke to me then, he was very disappointed they couldn’t get that work permit.
“Pep said: ‘You’ve got a really good lad there’. There is no better endorsement for the boy.”
Luiz had spent the past two seasons on loan with Girona and was suggested as a possible target by Villa's Spanish sporting director, Jesus Garcia Pitarch.
Where City had failed, Villa were able to secure a work permit via the FA Exemptions Panel's points-based system, which took into account the size of the fee, along with Luiz's salary and importance to the club's plans in their first season back in the Premier League.
City's continued admiration for the player is demonstrated by the presence of a buy-back clause in the deal but only a successful spell with Villa would see it triggered.
“We felt that when we’d spoken to Man City and with the figures they were looking for, we could go and process a work permit for him," explained Smith.
"That was the problem Man City had before. But there’s a totting up of points to get the permit and we just felt the points were there for us.
“The only delay was administrative, he had to go and get his passport sent from Brazil to the UK to get stamped with the visa.
"The work permit was given very early but it was then just about getting the passport back to him and getting him in the UK."
Luiz only arrived at Bodymoor Heath just two days before the season began but has featured in both matches so far and will make his second start on Friday when Everton visit Villa Park.
“He’s a really talented player but he’s also a very young player as well," said Smith. "We have to take our time nurturing him and helping him integrate into the squad and the team."