President Luis Guillermo Solis declared three days of mourning, starting Monday.
In neighboring Nicaragua, officials reported no casualties but dozens of homes were damaged in low-lying areas.
Hurricane Otto had sparked red alerts in both countries when it spun in from the Caribbean on Thursday with winds of up to 175 kilometres per hour.
It made landfall in southeastern Nicaragua, in an area with national reserves that is sparsely inhabited, before crossing into Costa Rica, losing strength as it went.
Early Friday it headed out into the Pacific Ocean as a downgraded tropical storm. It should continue to weaken, the US National Hurricane Center said.
A Costa Rican police official, Walter Espinoza, told a news conference: "The number of people killed is nine. We have recovered eight bodies, only one remains."
Solis said the storm dumped a month's worth of rain in just a few hours in Costa Rica. Authorities said it caused around $8 million in damage to roads.
Aerial television pictures from northern Costa Rica showed water and mud in several towns, and small bridges collapsed.
Evacuations
Updating an earlier death toll of four, Espinoza said five of the nine people killed died in Upala, a town near the border with Nicaragua that found itself in the storm's path.
An Upala resident, Juan, told the Repretel channel he lost his son when rising waters tore away his home on a river bank.
The other four died in Bagaces, a town 100 kilometres north of the capital San Jose.
In Nicaragua, the government's spokesperson, First Lady Rosario Murillo, said: "Up to now, thank God, we haven't counted any loss of human life."
Officials in both countries had evacuated the most at-risk areas before the hurricane hit, and closed schools and mobilized emergency crews.
Officials in Costa Rica said 5500 people had been put up in shelters.
Nicaragua had 44 shelters operating for many of the 10,500 people who had been evacuated.
UN agencies and non-governmental organizations had supported the emergency response, the UN office coordinating humanitarian affairs said in a statement.
Early this week, as Otto gathered strength in the Caribbean, its outer bands of wind and rain contributed to the deaths of eight people in Panama, according to the national civil protection service.
On Thursday, at the same time as the hurricane struck, a 7.0 earthquake was registered on the other side of the Central American isthmus, 120 kilometres offshore in the Pacific Ocean.
Although the temblor prompted panicked residents in El Salvador's capital to run out of buildings, and briefly sparked tsunami alerts in El Salvador and Nicaragua, no damage was reported.
The sole casualty was in Nicaragua, where one person died of a heart attack.
