The increased grant will mean an average increase of£175m per council in basic grant support to support front-line services.
Councils that meet targets on education, social services, transport and the environment will share an extra£30m, while£20m is to be set aside for a new deprivation grant.
The total increase in funding will average 8%, said Mrs Hart.
'In particular, Blaenau Gwent, an authority with significant areas of deprivation, has received additional resources for 2003-04 of just 4.7%, making additional investment in public services where it is most needed very difficult,' said a WLGA spokesman.
A spokesman for Cardiff CC said its settlement of 5.9% was partly based on census figures showing a population decline.