Kucinskis, who has been a member of various different political parties during his career, becomes the country's thirteenth Prime Minister since the restoration of independence from the Soviet Union in 1991.
Saeima approved him for the job by 60 votes to 32.
Speaking to reporters after the vote, Kucinskis said that Saeima's support for him amounts to an "advance payment of trust".
"I am at work already and have no time for pleasure," an urgent-sounding Kucinskis said, promising he'll be starting talks with the new ministers over their tasks in the new cabinet Friday.
Political analyst Ivars Ījabs told Latvian Television that Kucinskis "will use the chance to show himself".
"We should look at the new government with the most positive thoughts," Ījabs said, praising Kucinskis as "an adequate, patriotic and professional man".
Kucinskis, 54, of the Greens and farmers Alliance political grouping succeeds Laimdota Straujuma, 59, who resigned last December after serving nearly two years following a power-battle inside her Unity political party that ultimately saw the party losing the premiership.
Kucinskis' coalition also includes the right-wing National Alliance: the same coalition as Straujuma's but with a cabinet reshuffle.
Changes in the cabinet
Dana Reizniece-Ozola (Greens) takes over the key Finance Ministry after serving time at the Economics Ministry. She is seen as probable future Prime Minister.
Uldis Augulis (Greens), who has been Transport Minister and most recently Welfare Minister, will become Transport Minister again, taking over the position from which Anrijs Matīss (Unity) was sacked in November due to PM Laimdota Straujuma's dissatisfaction with Matiss' efforts to plot the future of airBaltic, Latvia's national airline.
Kārlis Šadurskis (Unity) moves to the Education Ministry. He is a senior politician who served at the same ministry from 2002 to 2004. Šadurskis was believed to be one of the likeliest potential candidates to become Prime Minister before Kucinskis was nominated.
Jānis Reirs (Unity) will move to the Welfare Ministry. He was the Finance Minister in the previous cabinet. Reirs turned down the PM nomination offered to him by president Raimonds Vejonis.
Arvils Ašeradens (Unity) takes over the Economics Ministry. Ašeradens previously served as the Parliamentary Secretary at the Finance Ministry.
The rest of the minister seats are unchanged.
Defense Minister Raimonds Bergmanis (Greens), Agriculture Minister Janis Duklavs (Greens), Health Minister Guntis Belevics (Greens), Foreign Minister Edgars Rinkevics (Unity), Interior Minister Rihards Kozlovskis (Unity), Culture Minister Dace Melbarde (National Alliance), Justice Minister Dzintars Rasnacs (National Alliance), and Minister for Environment and Regional Development Kaspars Gerhards (National Alliance) remain in their posts.