  We present an analysis of the levels and evolution of star formation activity
in a representative sample of 30 massive galaxy clusters at 0.15<z<0.30 from
the Local Cluster Substructure Survey (LoCuSS), combining wide-field Spitzer
24um data with extensive spectroscopy of cluster members. The specific-SFRs of
massive (M>10^10 M_sun) star-forming cluster galaxies within r200 are found to
be systematically 28% lower than their counterparts in the field at fixed
stellar mass and redshift, a difference significant at the 8.7-sigma level.
This is the unambiguous signature of star formation in most (and possibly all)
massive star-forming galaxies being slowly quenched upon accretion into massive
clusters, their SFRs declining exponentially on quenching time-scales in the
range 0.7-2.0 Gyr. We measure the mid-infrared Butcher-Oemler effect over the
redshift range 0.0-0.4, finding rapid evolution in the fraction (f_SF) of
massive (M_K<-23.1) cluster galaxies within r200 with SFRs>3M_sun/yr, of the
form f_SF (1+z)^7.6. We dissect the origins of the Butcher-Oemler effect,
revealing it to be due to the combination of a ~3x decline in the mean
specific-SFRs of star-forming cluster galaxies since z~0.3 with a ~1.5x
decrease in number density. Two-thirds of this reduction in the specific-SFRs
of star-forming cluster galaxies is due to the steady cosmic decline in the
specific-SFRs among those field galaxies accreted into the clusters. The
remaining one-third reflects an accelerated decline in the star formation
activity of galaxies within clusters. The slow quenching of star-formation in
cluster galaxies is consistent with a gradual shut down of star formation in
infalling spiral galaxies as they interact with the intra-cluster medium via
ram-pressure stripping or starvation mechanisms. We find no evidence for the
build-up of cluster S0 bulges via major nuclear star-burst episodes.
