The defender is convinced the Swans have found the right man to further develop their passing style and has backed the Dane to "reinforce" the squad this summer
The Swans took the Premier League by storm last season, finishing in 11th place and earning plaudits for their passing football under Rodgers - a success which earned the Northern Irishman the Liverpool job.
New coach Laudrup spent five years distinguished years as a player at Spanish giants Barcelona, a club with a distinct possession-based ethos, and the 29-year-old defender believes this will help the Dane to fit in.
Rangel told reporters: "The team needed a candidate to continue and Laudrup is the right person. Laudrup and Swansea have found each other.
"He has been at Barca and knows the game in which Swansea is based to some extent. He knows it's complicated, but we will get there and make it easy if we all pull in the same direction.”
Rangel is also expecting the former Getafe boss to bring in several signings this summer in order to build on the platform left by Rodgers.
He added: "No one can say that everything will go well, but you have to evolve, we have a good team and I guess signings will reinforce us."