Michu, whose full name is Miguel Perez Cuesta, agreed a three-year contract with the Premier League club and will complete his move to the Liberty Stadium subject to international clearance.
The 26-year-old, who passed a medical on Thursday, came to Laudrup's attention after scoring 15 goals from midfield in the Spanish top-flight last season.
Laudrup has now made three signings in the month since he succeeded Brendan Rodgers as Swansea manager.
Michu's capture follows the arrivals of defender Chico Flores and midfielder Jonathan de Guzman.
Laudrup believes former Oviedo and Celta Vigo star Michu, who had reportedly been a target for Manchester United, Liverpool, Sevilla and Valencia, will prove a real bargain for Swansea.
"It's a fantastic signing. We are talking about a player who scored 15 goals in the Spanish league last year for a small club. He was a big difference for them with his goals," Laudrup said.
"We lost (Gylfi) Sigurdsson, who played in that position for half a season, so to sign a player like Michu is fantastic for us when you look at the price and quality of the player. It is a bargain."
Source: AFP
Source: AFP