Campbell was heavily linked with Rovers' Championship rivals Hull in January but has now agreed terms on a 93-day deal at Ewood Park.
He has found himself down the pecking order at Rangers and has made just two appearances under Harry Redknapp, both coming in the FA Cup.
The 31-year-old enjoyed a fruitful loan spell with Ipswich during the tail end of 2012, scoring 10 goals in 17 appearances.
Williamson, 30, has signed a permanent deal with Michael Appleton's men until the summer of 2014.
The former Sheffield United midfielder has been without a club since he left Appleton's former employers Portsmouth last month.