Vasquez, 24, spent the 2014-15 season on loan at Espanyol, before returning to the Bernabeu last summer.
The attacker made 32 appearances for Real Madrid during the 2015-16 campaign and his performances in the final few months earned him a spot in the Spain squad for Euro 2016.
Despite the rivalry between Barcelona and Real Madrid, Alba has lavished praise on his new international teammate and claimed that Vasquez would be "an important player for any team".
"Besides the quality he has and how quick he is, Lucas' attacking and defensive work for his team stands out," Alba told reporters at an Adidas event. "He'd be an important player for any team because he can revolutionise a game at any moment, whether it be from the start or off the bench. I'd like to have Lucas Vazquez on my team."
Spain will open their Euro 2016 campaign against Czech Republic on June 13.