Al-Qaeda militants attacked the Splendid Hotel in the West African state’s capital, Ouagadougou, as well as a cafe and another hotel nearby.
Four of the attackers were killed, two of them reportedly women.
The siege at the Splendid was declared over after a joint operation by local and French security forces.
The Al-Qaeda in the Islamic Maghreb (AQIM) militant group has announced that it carried out the attack.
Bukinabe President Roch Kabore, who arrived at the scene on Saturday morning amid right security, announced the death toll and the liberation of at least 150 hostages.
French President Francois Hollande condemned the “odious” attack on the capital of the former French colony.
In November, an AQIM attack on a hotel in the Malian capital Bamako left 19 people dead.
In another development, two Austrian citizens, a doctor and his wife, were kidnapped overnight in northern Burkina Faso near the border with Mali, Burkinabe officials said.
The numerous armed groups in the Sahel often take advantage of the porous borders and weak regional security to establish their violent campaigns.
A recently consolidated AQIM – since mending relations with its offshoot, the al-Murabitoun group – is keen to cement its status as the dominant jihadist group in North Africa and the Sahel, particularly with the rise of its rival, the so-called Islamic State, in the region.
AQIM made this point in its purported attack on the Radisson Blu hotel in Mali’s capital Bamako in November. Mali has been a key theatre of operation but now its southern neighbour, Burkina Faso, is the latest victim.
Burkina Faso is only just moving on from a political crisis. Its new President, Roch Kabore, has only been in office for three weeks and already has his hands full.
Militants attacked the Splendid and the nearby Cappuccino cafe on Friday evening, setting off several explosions. Both places are popular with UN staff and foreigners.
Survivors described how the militants went from person to person, touching their bodies to see if they moved. Those that did were shot at close range.
Interior Minister Simon Compaore said 10 bodies had been found on the cafe terrace alone. He added that at least 33 hostages had been injured.
As the end of the siege at the Splendid was being announced, reports came in that militants had taken up position at the Yibi hotel, a short distance away. One attacker was killed at the Yibi, officials said later.
Remi Dandjinou, the Burkinabe communications minister, told the BBC earlier that between six and seven militants had attacked the Splendid, adding that they had been staying at the hotel as guests.
Interior Minister Compaore said two black Africans and an Arab were among the militants killed.
Burkina Faso recently held its first presidential election since a coup earlier last year.
That coup toppled long-time leader Blaise Compaore, who had governed for 27 years.
“We are still in a context of political fragility, so I think the timing of this attack is meaningful,” Cynthia Ohayon, an analyst with the International Crisis Group, told the BBC from Ouagadougou.
“The country has long borders with Mali and Niger, and we know there are armed groups present on the border, so this was probably something we had coming.”