Well, time required for medications to come in effect may differ from person to person. If the depression is situational then it may take less time but if the depression is complicated and the brain is not able to produce enough amount of serotonin then it may take longer time. Apart from this, it also depends on the type of medication.  There is no perfect way yet to determine the type of depression a person goes through. So they generally have to go with trial and error method in order to determine the exact cause.

There is no fix time as in how much time will it take for the medication to work for the depressed person. If the person reacts fast to the medication and is actually willing to come out the situation then the effect will be seen fast on them. On the other hand, if the person is not wiling to respond then it may take long time. Some people might even require taking the medicines for the rest of their lives. Typically it takes around five weeks for the medication to come into effect and according to the response of the patient the doctors prescribe further medicines.