About 1,000 arrived on Saturday alone, setting out on about 20 barely seaworthy boats.
One person was flown to hospital by helicopter.
There has been a sharp increase in the number of migrants from West Africa attempting to reach the Canary Islands in recent months.
The island chain is just 100km (60 miles) off the coast of North Africa.
According to the Spanish government, more than 11,000 arrivals have been recorded in the Canary Islands this year compared with 2,557 during the same period last year.
A spokeswoman for Canary services told AFP news agency the migrants had arrived on the islands of Gran Canaria, Tenerife and El Hierro.
The body of one person who died during the perilous journey was recovered by rescuers on El Hierro, the spokeswoman said.
Images taken from Arguineguin port in Gran Canarias this weekend show migrants queuing up to receive assistance.
Last month at least 140 migrants bound for Europe drowned after a boat carrying around 200 people sank off the coast of Senegal.
The boat caught fire and capsized shortly after leaving the town of Mbour, the International Organization for Migration (IOM) said.
About 60 people were rescued, according to reports.
It is believed the migrants were attempting to reach mainland Europe via the Canary Islands.
At least 414 people are known to have died along this route so far this year according to the IOM. A total of 210 fatalities were recorded on the same stretch in the whole of 2019.