Villa reportedly beat off competition from West Brom to land the 28-year-old who started all four games for his country in the World Cup in Brazil.
After one season in La Liga with Elche and an impressive campaign with Colombia, Sanchez agreed a four-year-deal at Villa Park on Friday but was not involved in their opening-day win over Stoke City.
Lambert is looking forward to welcoming the midfielder to his squad having been impressed by his qualities during the World Cup.
"Carlos is a great coup for Villa," he told the club's official website. "Carlos has real power - and he knows the role really, really well.
"He hasn't done too much since the World Cup but in Brazil I thought he was excellent in a team that took everyone by surprise.
"He comes with great pedigree and now it's up to use to get him up to speed and let him fit in.
"It's an opportunity for him and the great thing is he will do the simple things really well.
"He can spot the danger out there on the pitch.
"His physical strength, too, is something we will benefit from in the middle of the pitch and his role will be a really important one for the team. He's a strong, powerful lad.
"I am sure the group will welcome him and get him going.
"We've beaten other teams to bring him here to Villa and I'm delighted as we needed someone of his ilk to come in. He'll be an excellent player for the club."
Sanchez will now compete with the likes of Ashley Westwood, Fabian Delph and Karim El Ahmadi to be in Lambert's first-team plans.
