Battery Charging - Electrical Model
It sounds like you got the charging description of a lead-acid battery.  Other battery types need to be charged in different ways.

For the lead-acid case that you describe, all you need is a single power supply that is both voltage and current limited.  Initially the battery voltage will be low, so the power supply current limit kicks in.  Eventually the voltage reaches the float level, so the power supply starts regulating voltage and the battery draws less current than the limit.