Rovers agreed a fee of more than £3million for the 25-year-old, who has penned a four-year contract at Ewood Park.
Best believes Blackburn can follow the example of Newcastle and bounce back stronger from relegation.
The Ewood Park outfit ended an 11-season stay in the top flight.
Leon Best: "With Newcastle, I think the season we had in the Championship built us and made us better in the Premier League.
"Now I want to do the same thing here. Sometimes you need that wake-up call to go down and build a good squad, go back up and work together.
"Danny Murphy, ex-Portugal striker Nuno Gomes and Fabio Nunes are unbelievable signings.
"I used to watch Nuno Gomes in the Euros and the World Cup for Portugal and to be playing with him now is unbelievable.
"Obviously Danny Murphy, with the clubs that he's played for - and as I know myself from playing against him last season - is a fantastic player."